{
"cells": [
{
"cell_type": "markdown",
"metadata": {
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"source": [
"## Curves and Lines\n",
"\n",
"The rate of change of a function at a point has an important geometric meaning\n",
"that you will explore in this section. To do this, you’ll need to be able to plot\n",
"points, which is done with the command point.\n",
"\n",
"**Example 1.** To plot a point at the coordinates (1,2), use the command\n",
" `point([1,2])`. Notice that the coordinates are given as a list.\n",
"\n",
"**Example 2.** To plot a larger red point at the coordinates (-3,5), use the command\n",
"`point([-3,5], color=\"red\", size=40)`.\n",
"\n",
"**Exercise 1.** Plot the function $h(x) = 16x^2$ for values of x between 0 and 5.\n",
"Overlay the point (1,16) on the graph and make sure the point is visible."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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",
"text/plain": [
"Graphics object consisting of 2 graphics primitives"
]
},
"execution_count": 1,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"plot(16*x^2, (x, 0, 5)) + point([1,16], color=\"red\", size=40)
"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"Graphics object consisting of 2 graphics primitives"
]
},
"execution_count": 3,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"plot(16*x^2, (x, 0, 2)) + point([1,16], color=\"red\", size=40)
"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"Graphics object consisting of 2 graphics primitives"
]
},
"execution_count": 2,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"plot(16*x^2, (x, 0.5, 1.5)) + point([1,16], color=\"red\", size=40)
"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"collapsed": false
},
"outputs": [
],
"source": [
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false,
"deletable": false,
"editable": false
},
"source": [
"**Exercise 2.** Create an animation that zooms in on this point by reducing the\n",
"range of $x$. Use at least five different zoom levels. What do you observe?"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"Animation with 5 frames"
]
},
"execution_count": 7,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"plots=[]\n",
"[1,0.8,0.6,0.4,0.2]\n",
"for h in [1,0.8,0.6,0.4,0.2]:\n",
" r=plot(16*x^2, (x,1-h,1+h)) + point([1,16], color=\"red\", size=40)\n",
" plots.append(r)\n",
"a=animate (plots)\n",
"show(a)"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false,
"deletable": false,
"editable": false
},
"source": [
"You should have noticed that as you zoom in on the curve, it starts to look\n",
"like a straight line. (Some points on certain curves will not do this, which is\n",
"an important observation but not very common in mathematical biology.) The\n",
"question is what straight line it is.\n",
"\n",
"To answer this question, we want to plot lines with slopes corresponding to\n",
"the average rates of change we computed in the previous lab. Since we have a point and a\n",
"slope, this is most easily done using the point-slope equation for a line passing\n",
"through the point $(x_1,y_1)$. This equation is $y-y_1 = m(x-x_1)$. However, since\n",
"Sage’s plot command requires everything other than y to be on the right-hand\n",
"side of the equation, we have to rearrange it into $y = m(x - x_1) + y_1$.\n",
"\n",
"**Exercise 3.** Create an interactive that plots the function f(x) = $16x^2$ and\n",
"a line that passes through the point (1,16) and a second point on the function\n",
"whose $x$-coordinate is set by the slider. Describe what happens as the movable\n",
"point approaches the fixed one."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "8a7530a8a2064f82b260a926ee3edae1",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"Interactive function with 1 widget\n",
" x2: FloatSlider(value=2.0, descript…"
]
},
"execution_count": 1,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"var(\"x\")
f(x)=16*x^2
@interact
def secline1(x2=(0,5,.2)):
m=((f(x2))-16)/(x2-1)
b=(-x2*m+f(x2))
i=plot(f(x),(x,0,5))+plot(m*x+b, (x,0,5))+ point([x2,f(x2)], color=\"green\", size=40)
show(i)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
],
"source": [
"#as the slider is brought closer to the fixed line the difference in x value decreases until you get to 1. At this point the delta x value is zero and because of that the graph gives us an error."
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false,
"deletable": false,
"editable": false
},
"source": [
"**Exercise 4.** You can display a number on a plot using the text function. The\n",
"syntax to display the value val at point `pt` on a plot is `text(val, pt)`. (As in\n",
"other cases, you can give the coordinates of `pt` as a list.) Modify your interactive\n",
"so it computes and displays the slope of the line being plotted.\n",
"**HINT:** Use + to overlay text on a plot."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "49673a38089044d5a435da2e9f72fa8b",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"Interactive function with 1 widget\n",
" x2: FloatSlider(value=2.0, descript…"
]
},
"execution_count": 3,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"var(\"x\")
f(x)=16*x^2
@interact
def secline1(x2=(0,5,.2)):
m=((f(x2))-16)/(x2-1)
b=(-x2*m+f(x2))
i=plot(f(x),(x,0,5))+plot(m*x+b, (x,0,5))+ point([x2,f(x2)], color=\"green\", size=40)+text(m,[2,150])
show(i)"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false,
"deletable": false,
"editable": false
},
"source": [
"********************\n",
"********************\n",
"So far, we’ve been working with derivatives at single points. However, we\n",
"can compute the derivative of a function at all points on the function. We then\n",
"obtain a new function, $f'(x)$. Just like the number that gives the rate of change\n",
"of a function at a single point, $f'(x)$ is termed the derivative of $f(x)$.\n",
"\n",
"In Sagemath, derivatives are computed using the function `diff`. For example, to\n",
"find the derivative of $e^{3x}$ with respect to $x$ and assign it to fp(x) enter\n",
"`fp(x)=diff(e^(3*x),x)`. As usual with an assignment, to print the result you will\n",
"need to include an extra line where you print `print(fp(x))` or show `show(fp(x))` \n",
"it. You can evaluate it for a particular $x$ value using the usual function\n",
"evaluation notation `fp(2)` gives the value of the derivative at $x=2$.\n",
"\n",
"**Example 3.** What is the derivative of $f(x) = 5x^{16}$ at $x = 1.5$?"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false,
"deletable": false,
"editable": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"80*x^15"
]
},
"execution_count": 4,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"d(x)=diff(5*x^16,x)\n",
"show(d(x))"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false,
"deletable": false,
"editable": false
},
"outputs": [
{
"data": {
"text/plain": [
"35031.5112304688"
]
},
"execution_count": 5,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"d(1.5)"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false,
"deletable": false,
"editable": false
},
"source": [
"**Exercise 5.** Use Sagemath to find the derivatives of each of the following functions:\n",
"1. $f(x)=x^3$\n",
"2. $H(t)=200-16t^2$\n",
"3. $g(x)=\\frac{x^3-1}{x^2+1}$\n",
"4. $M(t)=10e^{2t}$\n",
"\n",
"Use show() to print out the formulas nicely. You may want to experiment with factor() and simplify() to see if you can get a nicer form for $g(x)$."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"3*x^2"
]
},
"execution_count": 9,
"metadata": {
},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"6.75000000000000"
]
},
"execution_count": 9,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"#1\n",
"f1(x)=diff(x^3,x)\n",
"show(f1(x))\n",
"\n",
"f1(1.5)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"-32*t"
]
},
"execution_count": 10,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"#2\n",
"H(t)=diff(200-16*t^2)\n",
"show(H(t))\n"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(x^3 - 1)/(x^2 + 1)"
]
},
"execution_count": 11,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"#3\n",
"var(\"X\")\n",
"simplify(x^3-1)/(x^2+1)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"3*x^2/(x^2 + 1) - 2*(x^3 - 1)*x/(x^2 + 1)^2"
]
},
"execution_count": 13,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"#3\n",
"g(x)=diff((x^3-1)/(x^2+1))\n",
"show(g(x))"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"20*e^(2*t)"
]
},
"execution_count": 14,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"#4\n",
"M(t)=diff(10*e^(2*t))\n",
"show(M(t))"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false,
"deletable": false,
"editable": false
},
"source": [
"In Example 4 we start with a function $f(x)=x^3+2x^2-x+1$ and use Sagemath to find the derivative $f'(x)$, and then plot $f(X)$ and $f'(x)$ between $x=-3$ and $x=2$ with legend labels. Execute the two cells below to see what they produce.\n",
"\n",
"**Example 4.**\n"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false,
"deletable": false,
"editable": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"'f(x)=' x^3 + 2*x^2 - x + 1"
]
},
"execution_count": 15,
"metadata": {
},
"output_type": "execute_result"
},
{
"data": {
"text/html": [
""
],
"text/plain": [
"\"f'(x)=\" 3*x^2 + 4*x - 1"
]
},
"execution_count": 15,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"f(x)=x^3+2*x^2-x+1 ## Our function\n",
"fp(x)=diff(f(x),x) ## fp(x) is the derivative\n",
"show(\"f(x)=\",f(x)) ## show the formula for f(x) in a pretty form\n",
"show(\"f'(x)=\",fp(x))## show the formula for f'(x) below it"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false,
"deletable": false,
"editable": false
},
"outputs": [
{
"data": {
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",
"text/plain": [
"Graphics object consisting of 2 graphics primitives"
]
},
"execution_count": 16,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"## Now we plot them and add legends\n",
"p1=plot(f(x),(x,-3,2),color='blue',legend_label=f(x)) ## generate the plot of f(x) from -3 to 2, store in p1\n",
"p2=plot(fp(x),(x,-3,2),color='red',legend_label=fp(x)) ## generate the plot of f'(x) from -3 to 2, store in p2\n",
"show(p1+p2,axes_labels=[\"x\",\"y/y'\"]) ## combine the plots and add axes labels"
]
},
{
"attachments": {
"ball_f_fp.png": {
"image/png": 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"
}
},
"cell_type": "markdown",
"metadata": {
"collapsed": false,
"deletable": false,
"editable": false
},
"source": [
"**Exercise 6.** Use the example above to create a function `plot_f_fp(f,xmin,xmax)` that takes as input a function f(x) and the range of x values for the plots and produces a plot with both $f(x)$ and $f'(x)$. Verify that it works correctly by checking that when you invoke it with `plot_f_fp(f,-3,2)` that it produces the same plot as in example 4, and that if you instead use \n",
"\n",
"`var('t'); H(t)=100-16*t^2; plot_f_fp(H,0,2.5)`\n",
"\n",
"you get a plot showing the height of a falling ball as on page 72 combined with a plot of the velocity of the ball which starts at 0 and goes linearly to -80 ft/sec.\n",
"\n",
""
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
],
"source": [
"def plot_f_fp(f,xmin,xmax):
fp(x)=diff(f(x),x)
show(\"f(x)=\",f(x))
show(\"fprime(x)=\",fp(x))
p1=plot(f(x),(x,xmin,xmax),color=\"blue\",legend_label=f(x))
p2=plot(fp(x),(x,xmin,xmax),color=\"red\",legend_label=fp(x))
show(p1+p2,axes_labels=[\"x\",\"y/y\"])
"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"'f(x)=' x^3 + 2*x^2 - x + 1"
]
},
"execution_count": 18,
"metadata": {
},
"output_type": "execute_result"
},
{
"data": {
"text/html": [
""
],
"text/plain": [
"'fprime(x)=' 3*x^2 + 4*x - 1"
]
},
"execution_count": 18,
"metadata": {
},
"output_type": "execute_result"
},
{
"data": {
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",
"text/plain": [
"Graphics object consisting of 2 graphics primitives"
]
},
"execution_count": 18,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"plot_f_fp(f,-3,3)"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
],
"source": [
"var('t')
H(t)=100-16*t^2
"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"'f(x)=' -16*x^2 + 100"
]
},
"execution_count": 24,
"metadata": {
},
"output_type": "execute_result"
},
{
"data": {
"text/html": [
""
],
"text/plain": [
"'fprime(x)=' -32*x"
]
},
"execution_count": 24,
"metadata": {
},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"Graphics object consisting of 2 graphics primitives"
]
},
"execution_count": 24,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"plot_f_fp(H,-3,3)"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false,
"deletable": false,
"editable": false
},
"source": [
"We know that the tangent line to a curve $y=f(x)$ at a point $a$ can be written down using the point slope form $y-y_0=m(x-x_0)$ where in this case the point $(x_0,y_0)=(a,f(a))$. We can rewrite that to get the formula for the tangent line as $y=f(a)+f'(a)(x-a)$.\n",
"\n",
"**Example 5.** Use $f(x)=x^3+2x^2-x+1$ and draw a graph showing the function f(x) and the tangent line to the function at $a=3/4$. We will add a dot showing the point of tangency."
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false,
"deletable": false,
"editable": false
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"Graphics object consisting of 3 graphics primitives"
]
},
"execution_count": 21,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"f(x)=x^3+2*x^2-x+1 ## Our function\n",
"fp(x)=diff(f(x),x) ## the derivative, f'\n",
"a=3/4\n",
"m=fp(a) ## slope of the tangent line\n",
"t(x)=f(a)+m*(x-a) ## formula for the tangent line\n",
"p1=plot(f(x),(x,-2,2),color='blue') ## generate the plot of f(x) from -2 to 2, store in p1\n",
"p2=plot(t(x),(x,-2,2),color='red') ## generate the plot of the tangent line from -2 to 2, store in p2\n",
"p3=point((a,f(a)),size=40,color='black') ## add a point, put it in p3\n",
"show(p1+p2+p3,axes_labels=[\"x\",\"y\"]) ## combine the plots and add axes labels"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false,
"deletable": false,
"editable": false
},
"source": [
"**Exercise 7.** Modify Example 5 to produce a plot showing the tangent line to $h(x)=\\frac{e^x-e^{-x}}{e^x+e^{-x}}$ at $x=1$. Plot from $x=-3$ to $x=3$."
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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3K/OJ1FSIj4e4uEsfx46dG4Iudpz13yxDwsPtyJXrzNuz3z/7bc6ckCOHHVdcceb9i30so/e54grLyOXLe+c19gaNMImIV4SHhxMeHu52GeJvNm+2Lt3Tp1sDylmz4Prr3a4qS9LS4PBh2L8fDh269HH48LlB6GJy5IDISDvy5bMlXKeOggXPvX2xI08eOy4UinLm1ABeVikwiYiI9yUk2N5vAwdC8eIwcaK1DfDD397Hj8Pu3bBvnx379595/+xj/36bivqnAgXgqqvOHGXLQrVq9vFTYehiR65cfvmSCApMIpJBx44dY8uWLadvb9u2jZUrV1KwYEFKly7tYmXi1xzH1iZ17gwHDkD37nbkzu1aOUeOWB/Mix0HD577mJw5bfqoWDEoWtTCz6nbxYpBkSJQqJCFoyuvtOkmCT5awyQiGTJnzhzq169/3sdbtWrFiAys3IyPjycyMlJrmELJxo3Qvr1Nu913HwwZAtde6/WnTU2FXbtg0yabAdy0yS7E274ddu48d0osVy4oXRrKlLHj1PslS9oVXMWK2ciQRn1EgUlEfEKBKYQcOwb9+8OgQVCqFAwdaoHJw5KTLQytXWvH+vVnwtGphdA5clhGu/56mxr7ZzAqUkRhSDJGgUlEfEKBKQQ4jnXmfvFFm9fq0QO6dbNhnMt04AAsW2bHmjUWkDZtOrOGqHhxqFjRrroqV84CUrlyFow0RSaeoG8jERG5fL//btNvP/0E//43DB5se8Blwf79Z8LRqePPP+1zBQpAlSpQvz60aweVKllQKljQg1+LyAUoMImISNYdPQqvvWbrk8qWtW7dmdhCx3FgwwaYPx9++cXebt9unytQAKpXhxYt7G2NGpbBNIUmblBgEhGRzHMcGDfO9nw7csQ2zH3xxXSn31JSYPnyM+Hol1+sT1G2bFC1qg1O3XKLwpH4HwUmERHJnHXrbD5szhx44AFb3F2mzAXvemoEaeZMu1huzhxryZQ7N9SuDW3aQL169n5EhE+/CpFMUWASEa+KjY0lNjaW1IxsLiX+LT4e+vWzq96uuca6dd9993l3O3ECfvwRJk2CadOsCWTOnPCvf8Err8Dtt1svo5w5ff8liGSVrpITEZ/QVXIBzHFgzBibfouPh969rRHlWVvfHDgAU6bYFnEzZ1pouv56aNzYMlW9erZth0ig0giTiIhc3Jo1Nv02bx48/DC8+671VsKaQ379NUyYAAsW2N3r1LHlTE2bQoUK7pUt4mkKTCIicr64OOjTB4YPh+uuswVId97JgQPw9XD46itbsB0ebiNIn35qvSmLFHG7cBHvUGASEZEzHAe+/NIaTh47Bm++SUrbTkz9MSefN7NpN7CQ9MUXdlWbZlglFCgwiYiIWbUK2raFX3+FRx9l47MD+WRaSb68xtYoVa9u7ZaaN7eNZkVCiQKTiEio+/tvW8j9/vukla/ArG4/8eqcO1h8JxQqBC1bwpNPQuXKbhcq4h4FJhGRUJWWBiNHwssvk3b8BLMavM1TKzuw5+0c3HMPjB9v65J0+b+IApOISGhavtym3xYuZEHZFvznyDscWlCc1q1tS7jy5d0uUMS/KDCJiISSw4dxer0CH33I1twVeYo57OQ2OgyAp5+2/dtE5HwKTCIioSAtjbRPPyOlaw9SEpJ4xRnE8spt6dwtB02bQvbsbhco4t8UmEREglza4qUcadGWq/5YzNe0ZHK9t2nzehSDb9XmtiIZlc3tAkRE5PIkJydf8OPOwUPsbPw81LqZP/9IpFvteZRf9CVfzYvittsUlkQyQ4FJRLwqNjaW6Ohoatas6XYpQSU5OZmYmBjKlClDeHg4V111FV26dOHQoUOQmsof3T4iPqockVPHMuyaoRydvYy3f6vHzTe7XblIYNLmuyLiE9p813NOnjxJkyZNmD59+nmfa1b8Ft46lkS5+GVMurIVed57iwYtimo0SeQyaQ2TiEiAGT9+/Hlh6SryEkNFnt7zG2uzV2JW31+5r/ctZNM8gohH6L+SiEiA+eKLL06/nw14npvZRA4eYhPtuYumUSe4q4/CkognaYRJRCTAHDx4EIBalCMWqM5i/sft9GAjfzGTPIfzuFugSBDS3x8iIgGmeqkK/I+bWcgmIDu1qcozzOEv9gIQHR3tboEiQUgjTCIigeLkSX7v+CFvfjeJNMJ4njv4hDmkkXbO3dq0aeNSgSLBS4FJRCQAxE39lb9btqX8kdVMK/EMqx6pyMdDOvPPC52ffvppWrdu7U6RIkFMgUlExJ/t38/ult0o8eMX/JG9BqtfWch9r91M4zBo8uQdfPzxx2zatImoqChat27N7bff7nbFIkFJfZhExCfUhymTTp4keej7pPbsTUJyDkZFx/DI9KcoXkqbvom4QSNMIiL+Zt48TjzTjvDNaxmR7b+ExfSnQ7er1CZAxEX67yci4i/27sV5rCXcdhurt+Sh5fWLqbv6A57trrAk4jb9FxQRr9JechmQkgKDB5NWrjxx38zgGT7luxcX8PmaGlSs6HZxIgJawyQiPqI1TBcxdy60bYvz+++MzPU8A/K+zvvjCnLHHW4XJiJn0xomERE37NkDXbvC2LHsKVOHpiwlb42qzB4HUVFuFyci/6QpORERX0pJgYEDoXx50mb9yPDqn1Nyxy806FqVn35SWBLxVxphEhHxlZ9/hnbtYONG/n6sLQ0XvsamLQWYMBH+/W+3ixORS9EIk4iIt/35Jzz6KDRoAFddxW+xy7n6h2HEZyvA4sUKSyKBQIFJRMRbkpPhrbegQgWYOxdn5BcMe2ge9dpVoXZtWLgQypVzu0gRyQgFJhERb5g1CypXhl694NlnObluIy8seJyOncLo3BkmT4YCBdwuUkQySmuYREQ8aedO6NIFxo+HW2+Fb74h4Zobad4cpk2D//0PnnrK7SJFJLMUmEREPCEpCd59F954AyIjYfRo+M9/+OtgGPfdAevWwZQpcPfdbhcqIlmhwCQicrmmT4cOHWDrVujYEfr0gfz5+eMPuOceOHoU5s2DatXcLlREskprmEREsmrHDnjgAWjUCEqUgFWrbJQpf34WL4Y6dSB7dvjtN4UlkUCnwCQiXhWUe8klJkL//nDDDbBoEYwdaz2W/n/jtylToH59uO46+PVXuPpql+sVkcumveRExCeCZi+5qVNt+m3HDujcGXr3hoiI058eOxYefxyaNIExYyB3bhdrFRGP0QiTiEhGbNtmHSYbN4ayZWH1anj77XPC0mefwWOPWWD69luFJZFgosAkInIpJ05Av34QHQ3Ll8PXX1uPpRtuOOdusbHw9NPw/PPWOiB7dpfqFRGvUGASEbmYH36wdUlvvAGdOsHvv8PDD0NY2Dl3e+cd2yKuSxcLTtn0k1Uk6Oi/tYjIP/3xB9x3HzRtCtdfD2vWQEwM5Mt3zt0cxwafunWDV16BgQPPy1IiEiQUmERETjl+HF591UaV1qyxbt3Tp0P58he8e79+0LevDUC9/rrCkkgwU+NKERHHge+/t6ve9uyBl16Cnj0hT56LPiQmxgJTTAx07+7DWkXEFQpMIhLaNm+2NgHTp1sDypkzbRruEgYPtjzVt6/Ckkio0JScSIh6//33ufrqq8mVKxfVq1dn/vz5F73vnDlzCAsLO+/YsGGDDyv2sIQE6NULKlWyxdwTJ1rHyXTC0vvv2+Lu7t1t9k5EQoNGmERC0FdffUWnTp14//33qVu3Lh999BGNGjVi/fr1lC5d+qKP27hx4zlNJwsXLuyLcj3LcWDCBJt+278fXn7Z0s8lpt9O+ewzaNvWLph7802tWRIJJer0LRKCatWqRbVq1fjggw9Of+yGG26gWbNmxMTEnHf/OXPmUL9+fY4cOUKBAgWy9Jx+0el70yZo396m3Ro3hqFD4dprM/TQ0aOtIeXzz1vrAIUlkdCiKTmREJOcnMyyZcto2LDhOR9v2LAhCxYsuORjq1atSlRUFA0aNGD27NmXvG9SUhLx8fHnHK5JSIAePWz6bfNmmDQJJk/OcFiaOBGeeAJat4bhwxWWREKRApNIiDl48CCpqakULVr0nI8XLVqUffv2XfAxUVFRfPzxx4wfP57vvvuO8uXL06BBA+bNm3fR54mJiSEyMvL0UapUKY9+HRniOPDNN1ChAgwZYmuW1q2zjd4y6JdfoHlzePBB+OQTNaUUCVVawyQSosL+MUziOM55HzulfPnylD+rF1GdOnXYtWsXAwcO5NZbb73gY3r06EGXLl1O346Pj/dtaPr9d5t+++kna0A5ZAhcfXWmTrF+vT20Th348kttdyISyvS3kkiIKVSoENmzZz9vNOnAgQPnjTpdSu3atdm8efNFPx8eHk7+/PnPOXzi6FFrvV25Mmzfble+ff99psPS7t1wzz1QsqStEQ8P9065IhIYFJhEQkzOnDmpXr06s2bNOufjs2bN4pZbbsnweVasWEFUVJSny8s6x4Fx42z6bfhw6NMH1q6Fe+/N9Kn+/ttaMgFMmwZZXOcuIkFEU3IiIahLly48/vjj1KhRgzp16vDxxx+zc+dOnn/+ecCm03bv3s0XX3wBwJAhQyhbtiwVK1YkOTmZUaNGMX78eMaPH+/ml3HGunU2/TZ7Ntx/v3WWLFMmS6dKSrJT/PmnrV8qUcLDtYpIQFJgEglBjz76KIcOHeK1115j7969VKpUialTp1Lm/0PG3r172blz5+n7Jycn07VrV3bv3k3u3LmpWLEiU6ZM4d4sjN54VHy87U8ybJhNuU2fDnffneXTpaXZ1XC//QY//gjR0R6sVUQCmvowiYhPeLQPk+PAmDG251tcHLzyirXfvoyFRo5jpxg6FL79Fh544PJKFJHgojVMIhJY1qyB22+Hli3hllvsargePS57Vfa779qFdMOHKyyJyPkUmEQkMMTF2XYmVavaliYzZ9pQ0CW2csmoceNssKpnT2jTxgO1ikjQ0RomEfFvjgOjRlmiOXbMNnHr1Aly5vTI6RcutA7eLVtC//4eOaWIBCGNMImI/1q1Cm691VZi33YbbNhgPZY8FJZ27oRmzaB6dfj0U215IiIXp8AkIv7n77+hQweoVg0OHbJL1r76yrpIesixY9bFO3duNaYUkfRpSk5EvCo2NpbY2FhSU1PTv3NaGnzxBbz8Mhw/Dm+9ZcHJQyNKZz/NY4/BH39YC4EiRTx6ehEJQmorICI+kW5bgRUroG1bSzD/+Q+8847XukZ2726nnzQJGjf2ylOISJDRlJyIuOvIEQtKNWpYI8rZs63HkpfC0qhRNnA1cKDCkohknKbkRMQdaWnw+ec23JOUZAmmXTvIkcNrT7liBTz7LLRqZRfaiYhklKbkRMQnzpmS27zZRpUWLbLr+d9+G7y8ke/BgzaIVbgwzJ8PuXJ59elEJMhoSk5EfKtTJ6hZ0xZ1z5sHX37p9bB08iQ0b25P+d13CksiknmakhMR70tLgxEj7P1vv7U9SNq0gSt88yOoRw+YM8e6E5Qq5ZOnFJEgo8AkIt61ZIlNvy1ZYreXL4frrvPZ048bZ8ujhgyxLehERLJCU3Ii4h0HD8Jzz0GtWpCSAjNm2Md92PRo1Sp46ilbJtWhg8+eVkSCkAKTiHhWaip8+CGUKwdffw3DhtnoUu3aPi3j8GG4/36oUAE++kjbnojI5dGUnIh4zsKFNv22fDk8+SQMGOBKG+3UVOt9GR8PP/8MefL4vAQRCTIaYRKRy/fXX/D001CnDjgOLFgAn33m2p4j/frZAu9x46BsWVdKEJEgo8AkIlmXmgqxsTb9NmECvP++Tb/VqXP6LrGxsURHR1OzZk2flDRjBvTvD6+/Dnfe6ZOnFJEQoMaVIpI1CxbY9NuqVTa6FBMDhQpd9O7p7iXnAbt2QdWqcPPNMHkyZNOfhCLiIfpxIiKZs38/tG4NdetaH6WFC+GTTy4ZlnwhJQUefdTWK335pcKSiHiWFn2LSMacPGlTbq++Ctmz26VnTz9t7/uB7t1tNnD+fLjqKrerEZFgo8AkIumbP982xl2zxnorvfGGX6WSCRNg0CAYPNjn3QtEJERo0FpELm7fPnjiCbj1VtuAbfFi67HkR2Hpjz9shvDBB6FjR7erEZFgpcAkIuc7edL2EilfHqa1SR8xAAAgAElEQVRNg08/hd9+gxo13K7sHImJ8PDDULgw/O9/ak4pIt6jKTkROdfcuTb9tm4dvPCCXZ9fsKDbVV1Q166wfr1luchIt6sRkWCmESYRMXv2wGOP2Q61+fLB0qXWY8lPw9KECVbeoEHWSkBExJsUmERCXUoKvPuuTb/NmmUdun/9FapVc7uyi9qxwzbVvf9+GwQTEfE2TcmJhLLZs236bcMGaNMGXnsNrrzS7aouKSXF9onLn1/rlkTEdxSYRELR7t3w4ovw1VfWgHLZMrjpJrerypA+fexivXnz/D7biUgQ0ZScSChJToa337bptzlzYORI67EUIGFp1iwYMMD2irvlFrerEZFQosAkEip+/BGqVIGePeGZZ2DjRuux5OU5LU9tvrt/Pzz+uG2o262bh4oTEckgbb4rEux27YIuXeDbb6FePRg+HCpX9nkZl7P5bloaNGpk+/yuWgVFi3qpSBGRi9AaJpFglZRk19z3728rpEeNghYtAnKV9NChMHMmzJihsCQi7lBgEglGM2dC+/a2b0jHjrZSOpOjOv5i5UrbWLdzZ2jY0O1qRCRUaQ2TSDDZscM2Vbv7bihe3Oav3n03YMPS8eM2KFahAsTEuF2NiIQyjTCJBIPERBg4EN580661HzsWHn00IKffzvbSS7Btm3U9CA93uxoRCWUKTCKBbto06NABtm+HTp3g1VchIsLtqi7b5Mnw/vu2/Ul0tNvViEio05ScSKDavh2aNYN774XSpW367Z13giIs7dsHTz4J992nrU9ExD8oMIkEmsRE28Lkhhtsg9yvv7YeS0EyDJOWBq1bQ/bs2vpERPyHpuREAsnkyXbV26neSq+8AvnyuV2VR733nrUPmDYNihRxuxoREaMRJpFAsHUrNGlix7XXwpo1tkdIkIWl1auti3fHjnDPPW5XIyJyhgKTiD87ccJ6KEVH2xqlb7+14Zfy5d2uzONOnLAWAuXLWxYUEfEnCkwi/shx4PvvLSgNGAAvvgi//249lgJsUU9G95Lr1g22bIExYyBXLh8VJyJB6ZlnniEsLIy77rqLC+0A9+qrrxIWFsaNN95IUlJShs6pveRE/M2WLdYmYNo0m5caOhTKlXO7qst2qb3kpk6Fxo1t/VK7di4VKCJB49ixY1SpUoWtW7cyePBgOnXqdPpzixYtom7dumTPnp3FixdTpUqVDJ1TI0wi/uL4cejdGypWhPXrYcIESxJBEJYuZf9+ayFw773Qtq3b1YhIMMiXLx9ffvkl2bNnp0ePHqxbtw6A48eP8/jjj5Oamsrrr7+e4bAECkwi7nMcC0fR0dZH6eWXLTA1axZw02+Z5TgWlgA++yzov1wR8aFbbrmFbt26kZiYSMuWLUlOTqZLly5s3ryZW2+9la5du2bqfJqSE3HTpk22Se7MmTbEMnQoXHed21V5xYWm5N57z2Yfp0yxL19ExJNSUlKoVasWK1as4K677mLWrFnkz5+f1atXU6ZMmUydSyNMIm5ISICePaFSJQtN339vPZaCNCxdyNq1tldc+/YKSyLiHTly5GDUqFHkypWLWbNmATBs2LBMhyXQCJOIbzkOjB9vTScPHIDu3W0KLndutyvzurNHmHLmzM/NN1tX7yVLQuLLFxGXJCcnc+ONN7Jp0yYiIyP5888/yZeFHnYaYRLxlQ0boGFDePhhuOkmW6fUt29IpoWePWHjRmshEIJfvoj4UK9evdi0aRPZsmUjLi6Ozp07Z+k8Ckwi3nbsmI0iVa5sHbsnT4ZJk+Caa9yuzBWzZ8PgwRATYy+JiIi3zJs3j0GDBpEnTx5mzZpFgQIF+PTTT/nhhx8yfS5NyYl4i+PYxrgvvgiHDtmwyksvhWxXxlNTcsWKxVGpUn5mzIBs+pNNRLwkPj6eKlWqsH37dmJjY2nTpg1jxozhscceo0iRIqxdu5bChQtn+Hz6cSXiDevXw513QvPmULOmdenu3TtkwxJYfgRITIQRIxSWRMS7OnTowPbt22nYsCFt2rQBoEWLFjz66KMcOHCA5557LlPny9IIk+M4HD16NLMPEwl+R4/aViYffABlysDbb8Ndd7ldlSuSkpLO2XLgiy8S6dXrej78cBf/+U/+SzxSRORcERERhGWiUduECRN44IEHuPLKK1m7di3Fixc//bkjR45QqVIl9uzZw2effcaTp5rBpcfJgri4OAfQoUOHDh06dOjw+hEXF5fhjLJv3z6nUKFCDuCMHTv2gveZMWOGExYW5kRERDjbtm3L0Hm9OsIUHx9PqVKl2LVr13l7R2VGzZo1WbJkSZYf78nz+Ms5/Om1DaZ/nyy9ruvXQ9eu8Ouv0LQpvPkmlCrlF1+Pp86RlfOcGmE6eRIeeigPe/fGs2fP1axfv54SJUr4rA5vnsdfzqGfB945h6deV0/U4k/n8MR5MvvaZnaEyRuuyMqDwsLCMvXNkz9//sv6ZsuePftlf7N66jz+co5T/OG1DbZ/H8jg6xoXZ20B3nsPrr0WZsywtgEerMVfznE553ntNVixAsaPT+L+++0Hn9vfs546j7+c4xT9PPBOLZf7unqqFn85hyfP44nX1leyFJh8ra2HduT0xHn85Rye4k9fjz/VckmOA6NH26jS0aPQvz907gzh4R6vxV/OkdXzLFxogemVV6BGjVTX6vDWefzlHJ7iT1+PP9XiCf7y9fjTv0+g8WpbgQvtHSWeodfWO9J9XVevhnbtYP58eOQRGDgQSpXyfaEB4Ngx68951VXwyy+wf/+fp4fgS5Ys6XZ5QUU/D7xDr6v3BOJr69ULe8PDw+nTpw/h//jLWy6fXlvvuOjr+vff0LEjVKsGBw/Cjz/CV18pLF1Cp06wb58NxuXIwenXVN+znqefB96h19V7AvG1VeNKkUtJS4Mvv4Ru3WzD3D59LDjlzOl2ZX5twgR44AH49FN4+mn7WCD+RSkicopax4lczMqVUK8etG4Nd9xhm5+99JLCUjr27IFnnoFmzeCpp9yuRkTEMxSYRP7pyBFbp1S9uk3F/fwzjB0Ll3EpfKhIS4Mnn7T17598Ai5fBSwi4jEBcZWciE+kpdmeHd272/4d77wD7dvbAhzJkPfeg5kzYfp0KFTI7WpERDxHI0wiAMuXQ926tuCmYUObfuvSRWEpE9auhZdfhg4d4O673a5GRMSzFJgktB0+DG3aQI0atqh77lwYNQqiotyuLKAkJcFjj8F119lWeiIiwcargalv375UqFCBvHnzcuWVV3LnnXeyaNEibz5l0EtJSeHll1/mxhtvJG/evBQvXpwnnniCPXv2uF1aYElLs0U25crZde+DB8Py5Xx38CB33303hQoVIiwsjJUrV7pdaUDo2RM2bLCXMndut6sJHfPmzaNJkyYUL16csLAwJk6c6HZJQSEmJoaaNWsSERFBkSJFaNasGRs3bnS7rKDwwQcfULly5dMdvuvUqcO0adPcLitDvBqYypUrx/Dhw1mzZg2//PILZcuWpWHDhvz111/efNqgdvz4cZYvX07v3r1Zvnw53333HZs2baJp06ZulxY4liyB2rXhueegcWObfuvYEa64goSEBOrWrcsADZNk2E8/waBBtoVelSrnfz42Npbo6Ghq1qzp++KCXEJCAlWqVGH48OFulxJU5s6dS9u2bVm4cCGzZs3i5MmTNGzYkISEBLdLC3glS5ZkwIABLF26lKVLl3LHHXfw73//m3Xr1rldWrp82ofpVB+WH3/8kQYNGvjqaYPekiVLuPnmm9mxYwelS5d2uxz/deiQDYV88glUrgzDh8O//nXBu27fvp2rr76aFStWcNNNN/m40MBx+LC9lBUq2GLvbJf4E0x9mLwrLCyMCRMm0KxZM7dLCTp//fUXRYoUYe7cudx6661ulxN0ChYsyDvvvMPTp5q2+SmfXSWXnJzMxx9/TGRkJFUu9GeoZFlcXBxhYWEUKFDA7VL8U2qqdVDs2dPeHzYMnn8ertBFopfDceC//4Xjx+3iwkuFJZFAFhcXB9gvdvGc1NRUvvnmGxISEqhTp47b5aTL678xJk+eTPPmzTl+/DhRUVHMmjWLQrre2GMSExPp3r07LVq00F/tF7JoEbRtC8uWWYOgAQOgSBG3qwoKI0fCt9/C11+DtoaTYOU4Dl26dOFf//oXlSpVcrucoLBmzRrq1KlDYmIi+fLlY8KECURHR7tdVro89jfh6NGjyZcv3+lj/vz5ANSvX5+VK1eyYMEC7rnnHh555BEOHDjgqacNehd7XcEWgDdv3py0tDTef/99F6v0Q3/9Ze2ma9e2Bd4LFsBnn50Tli712sqlbdpkvT1bt4aHH3a7GhHvadeuHatXr2bs2LFulxI0ypcvz8qVK1m4cCEvvPACrVq1Yv369W6XlS6PrWE6evQo+/fvP327RIkS5L7A5TLXX389Tz31FD169PDE0wa9i72uKSkpPPLII2zdupWff/6Zq666ysUq/UhqKnz0EfTqZbffeMPmjbJnP++ul/qe1Rqmi0tKgjp1rAvDsmWQL1/GHqc1TN6lNUye1759eyZOnMi8efO4+uqr3S4naN15551ce+21fPTRR26Xckkem5KLiIggIiIi3fs5jkNSUpKnnjboXeh1PRWWNm/ezOzZsxWWTvntN5t+W7HCGlDGxEDhwhe9e0a/Z+VcPXrAunWwcGHGw5JIIHEch/bt2zNhwgTmzJmjsORlgZILvLaGKSEhgTfeeIOmTZsSFRXFoUOHeP/99/nzzz95WGP4WXby5Ekeeughli9fzuTJk0lNTWXfvn2ALUjMGYobwx44YC2mR4yw/d8WLoRatbJ0qsOHD7Nz587Tfa1O9V4pVqwYxYoV81TFAWvqVGtZNXgwVK3qdjVy7NgxtmzZcvr2tm3bWLlyJQULFtQVs5ehbdu2jBkzhu+//56IiIjTP2MjIyMvOHMiGdezZ08aNWpEqVKlOHr0KOPGjWPOnDlMnz7d7dLS53jJiRMnnPvvv98pXry4kzNnTicqKspp2rSps3jxYm89ZUjYtm2bA1zwmD17ttvl+VZKiuMMG+Y4kZGOU7Cg43z4oeOcPHlZp/z8888v+Nr26dPHMzUHsD17HKdwYce5917HSUvL/OPj4uIcwImLi/N8cSFq9uzZF/x+bdWqldulBbSL/Yz9/PPP3S4t4D311FNOmTJlnJw5czqFCxd2GjRo4MycOdPtsjLEp32YRDzm119t+m31anj2WeuaqKlJr0lLs/3h1q6FVauydqGh1jCJSCBT5xQJLPv2QatW1nAyZ05rG/DRRwpLXvbOO9bRe9QodWUQkdCkwCSB4eRJGDIEypeHKVOsW/fChaDtNrxu0SJ45RVbJqYG/SISqjQlJ/5v3jxr+rN2rXXo7t8f1HHXJ+LibHF34cLwyy+QI0fmzxEbG0tsbCypqals2rRJU3IiEpAUmMR/7d0LL70Eo0dbA8rYWKhWze2qQobjwGOPweTJsHIlXHPN5Z1Pa5hEJJBpMy3xPykp8N570LcvhIdbh+5WrbRZmY998QWMHQtjxlx+WBIRCXQKTOJf5syx6bfff4cXXoDXX4crr3S7qpCzYYNdhNi6NfznP25XIyLiPv3JLv5h9277zVy/PkRG2p4bw4crLLng+HHbH65UKRvoExERjTCJ25KTYehQeO01yJPHunU//rim31zUvj388QcsXqytT0RETlFgEvf89JNNv23aZG/79YMCBdyuKqSNHGlLxj7/HCpVcrsaERH/oT/jxff+/BMeeQTuvBMKFbLNcocOVVhy2bp1tmysdWs7RETkDAUm8Z3kZBgwwJpPzp8PX35pPZYqV3a7spB37JitW7rmGuveICIi59KUnPjGzJlnFsd06GAtA9SLxy84DrRpAzt3wpIltpRMRETOpREm8a6dO+HBB23n1qgo64A4aJDCkh/57DMb7PvwQ7jhBrerERHxTwpM4h1JSfDmm1ChAvz2m3U/nD1bK4n9zIoVtt7+2WehZUu3qxER8V8KTOJ506fDjTdCnz7W/XDjRuuxFBbmdmVylkOH4IEHoGJFGDbMe88TGxtLdHQ0NbVRsogEMO0lJ56zfTt07gwTJ1oDyuHDITra7arkAlJToXFjWLrUeoSWKeP959ReciISyDTCJJcvMdG2MLnhBls1PG6c9VhSWPJbffvCrFm2V5wvwpKISKDTVXJyeaZMgY4dbXF3587Qu7faQ/u5SZOgf39bYnbXXW5XIyISGDTCJFmzdSs0bQr33QdXXw2rV8Nbbyks+bnNm23nmWbNoHt3t6sREQkcCkySOSdO2HxOdLS1CPjmG+uxVKGC25VJOhISbJF3sWK2ZZ/W4IuIZJym5CTjfvjBpt/+/BO6doVevSBvXrerkgxwHHjmGdi2DRYtgshItysSEQksCkySvi1boFMnW690993WNqBcOberkkwYMMDW4n/9tbUREBGRzNGUnFzc8eO2iLtiRVizBr77DqZNU1gKMN9/Dz17wquv2n5xIiKSeRphkvM5jv2W7dQJ9u6Fbt2gRw9tMhaAVq+Gxx6z3Wn69HG7GhGRwKXAJOfavNk2x50+He69F378Ea67zu2qJAsOHLALGa+/HkaOhGwaTxYRyTL9CBWTkGCLuCtVgg0bbIRp8mSFpQCVlGRXxCUm2j+l1uaLiFwejTCFOsextUmdO9uQRPfuduTO7XZlkkWOAy+8YE3X58yB0qXdrkhEJPBphCmUbdxoV7099BBUqQLr1kG/fgpLAW7wYPj8c/jkE6hTx+1qtPmuiAQHbb4bio4ds70xBg2CUqVg6FDr2C0Bb+pUaNLE2mS99Zbb1ZxLm++KSCDTlFwocRzrzP3ii3DwILzyil0BlyuX25WJB6xaBc2bQ6NGtk+ciIh4jqbkQsXvv9tOq48+CtWrw/r11phHYSko7NxpFzVefz2MHQvZs7tdkYhIcFFgCnZHj8JLL0HlyrBjh83ZTJxoG+ZKUDhyxEaVcua0ZuwREW5XJCISfDQlF6wcx/bC6NrVfqP27WtTcRpRCiqJidCsGezbBwsW2Ma6IiLieRphCkbr1sEdd0CLFlC7tk3H9eqlsBRk0tKgVStYvBgmTYLy5d2uSEQkeCkwBZP4eBtFqlIF9uyBGTNg/HgoU8btysQLXnrJ1vCPGQN167pdjYhIcFNgCgaOA6NH2xDDhx9ay4DVq6FhQ7crEy8ZMsS6QgwbBvffn7nHOo5D3759KV68OLlz5+b2229n3bp1l3zMiBEjCAsLO+9ITEy8jK9CRCRwKDAFujVr4PbboWVLqFfPtjXp3h3Cw92uTLzkm2+gSxfrCNGuXeYf//bbbzNo0CCGDx/OkiVLKFasGHfddRdHjx695OPy58/P3r17zzlyaZpXREKEAlOgiouDTp2galXYvx9mzYKvv7ZGlBK0pk6Fxx6z5WkxMZl/vOM4DBkyhF69evHAAw9QqVIlRo4cyfHjxxkzZswlHxsWFkaxYsXOOUREQoUCU6BxHPjiC5t++/RT+625ejXceafblYmXzZkDDz5o/ZY+/xyyZeF/77Zt29i3bx8Nz5quDQ8P57bbbmPBggWXfOyxY8coU6YMJUuW5L777mPFihWXvH9SUhLx8fHnHCIigUqBKZCsWmXTbq1aQf36thfcSy9ZAx4JaosW2ZYn9erBV19BjhxZO8++ffsAKFq06DkfL1q06OnPXUiFChUYMWIEkyZNYuzYseTKlYu6deuyefPmiz4mJiaGyMjI00cpjX6KSABTYAoEf/8N7dtDtWrWU+nnn62dc4kSblcmPrBqFdxzD9x0E0yYkLnlaaNHjyZfvnynj5SUFMCm187mOM55Hztb7dq1admyJVWqVKFevXp8/fXXlCtXjvfee++ij+nRowdxcXGnj127dmW8cBERP6PGlf4sLQ1GjoSXX4YTJ+Dtt6FDh6wPL0jA2bjRdrS59lqYPBny5s3c45s2bUqtWrVO305KSgJspCkqKur0xw8cOHDeqNOlZMuWjZo1a15yhCk8PJxwXXwgIkFCI0z+avly+Ne/4Kmn7Dfmxo3WY0lhKWRs325L04oUgenTITIy8+eIiIjguuuuO31ER0dTrFgxZs2adfo+ycnJzJ07l1tuuSXD53Uch5UrV54TukREgpkCk785fBjatIEaNWwfuDlzrMdS8eJuVyY+tHWrdYsID7cLIAsV8sx5w8LC6NSpE2+++SYTJkxg7dq1tG7dmjx58tCiRYvT93viiSfo0aPH6dv9+vVjxowZbN26lZUrV/L000+zcuVKnn/+ec8UJiLi5zQl5y/S0uCzz6BHD0hOtq6EbdtqRCkEbdliO9vkymXL1Tw9iNOtWzdOnDhBmzZtOHLkCLVq1WLmzJlEnLVr786dO8l21mV4f//9N8899xz79u0jMjKSqlWrMm/ePG6++WbPFici4qfCHMdx3C4i5C1dauFo8WJ4/HFbq6QeNyFp0ya7ADIiwsJSMA0sxsfHExkZSVxcHPnz53e7HBGRTNGUnJsOHYLnn4ebb7Zt5+fPtx5LCkshacMGuO02KFDAZmKDKSyJiAQ6Tcm5ITUV/vc/m347eRKGDoUXXoAr9M8Rqtats2m4okXhxx9tobeIiPgPjTD52uLFULs2/Pe/0LSpzcG0b6+wFMKWLrUF3lFRNg2nsCQi4n8UmHzl4EF49lkLSydPwq+/2v4Wmeh9I8Fn9mxbs3TddRaWPHU1nIiIeJYCk7elpsIHH0C5cvDttzB8uA0pZKLnjQSniROhUSP7VvjxRyhY0O2KRETkYhSYvGnhQlvQ3aYN3H+/Tb+1aQPZs7tdmbjsk0/goYdsVnbSpMx38A4ksbGxREdHU7NmTbdLERHJMrUV8IYDB6B7d5tyq1YNYmNtKk5CXloa9OwJb71l2XnYsNDJz2orICKBTCuNPenkSfjwQ+jdG8LCbCru2WdD5zeiXFJiIrRqBd98Y31JO3WybxMREfF/Ckye8uuv1nxy9Wp45hl4802t4JXTDh6EZs1g2TJbyvbAA25XJCIimaE1TJdr/34bNvjXvyBnTli0CD7+WGFJTtu8GerUsSVsc+YoLImIBCIFpqw6edIWoJQrB1OmWEhauBC0sFXO8ssvFpayZ7dvj1q13K5IRESyQoEpK+bNs8XcnTpBixawcaOtVcqml1PO+OQT695dqRIsWADXXON2RSIiklX6DZ8Ze/dCy5a24VeePNa1+4MP4Kqr3K5M/Ehysl0B99xzlqNnzlSPJRGRQKdF3xmRkmINJ/v0gfBw2weudWuNKMl5duyARx6BFStslvbZZ92uSEREPEGBKT1z59rVb7//bhvkvv46XHml21WJH5o8GZ54AvLnt4smtZxNRCR4aIjkYvbssfVJt99uvwGXLrVRJoUl+YeTJ61PaZMmdrHkihUKSyIiwUYjTP+UkgJDh0K/fpA7t3XrfuIJTb/JBe3ZA82b26Lud96BF19UM0oRkWCkwHS2n3+Gdu3sqre2beG116BAAberEj81daotZcuZ02Zu69Z1uyIREfEWDZsA/PknPPooNGhgV7wtX249lhSW5AKOHYP//hcaN4YaNWwKTmHp4rT5rogEg9DefDc5GQYPtoXc+fLZnErLlppTkYtasMBmaPfutf3gnntO3y4Zpc13RSSQhe4I06xZULky9Opl135v3AiPP67ffnJBycnQsyfUqwdFisCqVTbKpG8XEZHQEHqBadcuePhhaNgQiha1+ZTBgyEy0u3KxE8tWWJXvQ0cCP37W6P3665zuyoREfGl0AlMSUkQEwMVKliTnNGjbSfUG290uzLxUwkJ0KUL1K5te8EtXgw9esAVulRCRCTkhMaP/unToUMH2LYNOnaEV1+13koiF+A48MMP9q2yfz+89ZZtG6igJCISuoJ7hGnHDnjgAWjUCEqWtIUnAwcqLMlFbd5sV7/9+99QrhysWQNduyosiYiEuuAMTImJttjkhhtg0SIYNw5++gmio92uTPxUQoKt/69UCdavhwkTbGDy2mvdrkxERPxB8P3dPHWqTb/t2AGdO0Pv3hAR4XZV4qdSU2HMGAtLBw7YFicvvwx58rhdmYiI+JPgGWHats3mURo3hrJlYfVqePtthSW5IMexbF2tmvVVqlHDRpb69VNYEhGR8wV+YDpxwn7LRUdbh+6vv7YeSzfc4HZl4qcWLYL69S1bFygAv/0G330H11zjdmUiIuKvAjsw/fADVKwIb7xhlzFt2GA9ltRNUC5g/Xp48EFrE3D4MEyZYp0latd2uzIREfF3gRmY/vgD7rsPmjaF66+3S5liYiBvXrcrEz+0apXl6EqVYOlSGDnS+pXee6+ytS9oLzkRCQaBtZfc8eMwYICtTSpa1Dp033+/fuvJBS1aBG++CZMmwdVXW9PJVq0gZ063KwtN2ktORAJZYFwl5zj2W69TJ9izB156yTb20upc+YfUVPj+e9sY99dfbQByxAho0QJy5HC7OhERCVT+PyV3qpNgs2a2kHvtWuuxpLAkZzl6FIYNs4D04IO2lcmECfD77zaqpLAkIiKXw39HmBISbD5l4EAoXhwmTrQ1S5p+k7OsXQuffmqjSAkJ8MgjdqFkjRpuVyYiIsHE/wKT49jQQOfOtpFX9+525M7tdmXiJ44ds+btn35q65SKFIHnn4e2baFUKberExGRYORfgWnTJmjfHmbOtKvghgzR3hQCWI5evNhC0rhxNpp0zz0wfrx9q2ght4iIeJN/BKaEBFuX9O67tknupEnQpInbVYkf2LTJAtK4cbYeqVQp2wz3ySehdGm3qxMRkVDhbmByHPj2W+jSBQ4etA29unXT9FuI27ULvvoKxo615u358tma/0GD4K67bEG3iIiIL7kXmH7/3abffvrJFnMPGWLNciTkOI41l5w0yY5lyyA83KbaevSwiySVoUVExE2+D0xHj8Lrr1vTyTJlbH+Ke+/1eRnirm8nEAsAAAStSURBVKQkmDv3TEjatQvy54dGjWzA8b777LaIiIg/8F1gchybZ3nxRThyBPr0scUouXL5rARxj+PYeqRZs2xN/+zZdrVbmTI23da0Kdx6qxZvi4iIf/JNYFq3zqbfZs+2rUxOjS5J0HIc2LgRfvnFjtmzYedOayBZt65Ntd13H9x4o1prBbvY2FhiY2NJTU11uxQRkSzz7l5y8fHQr5+1YL76anjvPbj7bq89nbgnJQVWroT588+EpL/+gmzZ4KaboF49aNjQRpHy5XO7WnGD9pITkUDmvREmx7Hfjps3w2uv2cKU8HCvPZ34juPA9u22OHvZMliyBH77zfZGzpULateG//7XQlLt2lqLJCIigc+7I0w//WSbe6lhTsA6eRK2bIE1a+wS/6VL7e3hw/b5EiVsG5K6dS0gVaumdUhyYRphEpFA5t3AJAEjNRW2bbPlZmvX2tt162DDBkhOtvuUKAHVq9tRo4a9LVrU3bolcCgwiUgg849O3+ITjmPrijZvPnNs2nTm7YkTdr8CBaBiRahTB555BipVsttFirhbv4iIiFsUmIKI49h+xTt22LF9+/lvExLO3L9kSZsxrVULnnjCglGlShAVpSvXREREzqbAFAAcB/7+G/buhT177O2Fjl27IDHxzOPy54eyZa2DQ/369n7ZslCunO1pnCePS1+QiIhIgFFgckFSEhw6ZMfBg+e+/ef7+/dbGEpKOvcckZE2EhQVZRvS3nyzvS1Txo6yZW1qTURERC6fAlMmpKbapfMJCXbEx9sRF3fm7dnvX+hzhw5Zh+t/ypYNrrrKjkKF7G2lSjYydCoYFS9ub4sV0+iQ+NZ3333HRx99xLJlyzh06BArVqzgpptucrssERGfCbjA5DgWXFJSzhxJSXYkJtpx9vv/vH2hz504cSYEJSScG4rO/tjZ010XkiOHjfzkz3/u2zJl7G1k5Pmh6NTbyEgLTSL+KCEhgbp16/Lwww/z7LPPul2OiIjPeTUw9e8PW7eeG25SUqy3zz8/lt7nzv54VoWFWWPF8HB7e/aRN6+N2uTNawEmb95zj1OfO/v4ZzAKD9diaQlOjz/+OADbt293txAREZd4NTCdulw9R45zj/Bw2x7jnx/PkQOuuCLzHz8Vev4ZhM6+HR5u91egEfGNpKQkks5afBcfH+9iNSIil8ergWnkSG+eXUT8WUxMDP369XO7DBERj9CqGRE5x+jRo8mXL9/pY/78+Vk6T48ePYiLizt97Nq1y8OVioj4TsAt+hYR72ratCm1atU6fbtEiRJZOk94eDjh2nBbRIKEApOInCMiIoKIiAi3yxAR8SsKTCKSrsOHD7Nz50727NkDwMaNGwEoVqwYxYoVc7M0ERGf0BomEUnXpEmTqFq1Ko0bNwagefPmVK1alQ8//NDlykREfCPMcRzH7SJEJPjFx8cTGRlJXFwc+fPnd7scEZFMUWASEZ9wHIejR48SERFBmBqiiUiAUWASERERSYfWMImIiIikQ4FJREREJB0KTCIiIiLpUGASERERSYcCk4iIiEg6FJhERERE0qHAJCIiIpIOBSYRERGRdCgwiYiIiKRDgUlEREQkHf8HmMahuyXdCzYAAAAASUVORK5CYII=",
"text/plain": [
"Graphics object consisting of 3 graphics primitives"
]
},
"execution_count": 22,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"f(x)=(e^x-e^-x)/(e^x+e^-x)
fp(x)=diff(f(x),x)
a=1
m=fp(a)
t(x)=f(a)+m*(x-a)
p1=plot(f(x),(x,-3,3),color='blue')
p2=plot(t(x),(x,-3,3),color='red')
p3=point((a,f(a)),size=40,color='black')
show(p1+p2+p3,axes_labels=[\"x\",\"y\"])"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"source": [
"**Exercise 8.** Use `diff` to create an animation showing the\n",
"tangent line to a function at different points, like the one at\n",
".\n",
"(You don't need to make the line change color.)"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"WARNING: Some output was deleted.\n"
]
}
],
"source": [
"f(x)=(e^x-e^-x)/(e^x+e^-x)
fp(x)=diff(f(x),x)
plots=[]
for a in srange(-3,3,.1):
m=fp(a)
t(x)=f(a)+m*(x-a)
p1=plot(f(x),(x,-3,3),color='pink',ymin=-1.5,ymax=1.5)
p2=plot(t(x),(x,-3,3),color='red',ymin=-1.5,ymax=1.5)
p3=point((a,f(a)),size=40,color='black')
p=p1+p2+p3
plots.append(p)
a=animate(plots)
show(a)"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"collapsed": false
},
"outputs": [
],
"source": [
]
}
],
"metadata": {
"kernelspec": {
"display_name": "SageMath 9.1",
"language": "sagemath",
"metadata": {
"cocalc": {
"description": "Open-source mathematical software system",
"priority": 10,
"url": "https://www.sagemath.org/"
}
},
"name": "sage-9.1"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 4
}