CoCalc Public FilesLab 5 / newLab5-turnin-1.sagewsOpen with one click!
Author: Derek Rivas
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# Lab 5: # Name: Derek Rivas # I worked on this code with: # Please do all of your work for this week's lab in this worksheet. If # you wish to create other worksheets for scratch work, you can, but # this is the one that will be graded. You do not need to do anything # to turn in your lab. It will be collected by your TA at the beginning # of (or right before) next week’s lab. # Be sure to clearly label which question you are answering as you go and to # use enough comments that you and the grader can understand your code.
#1 %auto typeset_mode(True, display=False) def weird_function(): pieces = [sin(x), cos(x), arctan(x), ln(x), sqrt(x), exp(x)] f(x)=prod([choice(pieces) for i in range(5)]) + prod([choice(pieces) for i in range(5)]) return f h(x)=weird_function()
#2 x1=3.5 x2=5.5 f_avg(x)=(h(x2)-h(x1))/((x2-x1)) f_avg
x  2.38517850947403×107x \ {\mapsto}\ 2.38517850947403 \times 10^{7}
#3 x1=3.5 deltax=[0.1, 0.01, 0.001] finst=[] for i in deltax: val=(h(x1+i)-h(x1))/i finst.append(val) finst
[330873.802234064330873.802234064, 285624.516938263285624.516938263, 281557.678575831281557.678575831]
#4 x3=1.2 deltax=[0.1, 0.01, 0.001, 0.0001] finst=[] for i in deltax: val=(h(x3+i)-h(x3))/i finst.append(val) finst #values approach 136 as it gets closer to zero
[164.024537585464164.024537585464, 138.686997792651138.686997792651, 136.432307573045136.432307573045, 136.209400933254136.209400933254]
#5 f(t)=1000*t^2 t1=1 deltat=[1, 0.1, 0.01, 0.001] finst=[] for i in deltat: val=(f(t1+i)-f(t1))/i finst.append(val) finst
[30003000, 2100.000000000002100.00000000000, 2010.000000000002010.00000000000, 2000.999999999752000.99999999975]
#6 g(t)=1000000*t^2 t1=1 deltat=[0.1,0.01,0.001] finst=[] for i in deltatime: val=((f(t1+i)-f(t1))/i) finst.append(val) finst
[2100.000000000002100.00000000000, 2010.000000000002010.00000000000, 2000.999999999752000.99999999975]
#7 #the limit allows for us to find a way to find only one order pair, if we use a small deltax it would still be only using another point #the smallest deltax is still not zero
#8 x^3*x^7
x10x^{10}
#9 type("x")
<type 'str'>
#10 factor(x^2+7*x+6)
(x+6)(x+1){\left(x + 6\right)} {\left(x + 1\right)}
#11 var("k")
kk
factor(k^2-5*k+6)
(k2)(k3){\left(k - 2\right)} {\left(k - 3\right)}
#12 var("n")
nn
f(n)=2^n plot(f(n), n,0,4, axes_labels=["n", "f(n)"])
#13 #the line is y=8 instead of another value of y because the points were plotted to have y as 8 and x at 0 along with the slope being zero
#14 h(x)=16*x^2 plot(h(x), (x, 0,5))+point([1,16], size=30)
#15 plots=[] x_zooms=[5,4,3,2,1] for i in x_zooms: p=plot(16*x^2, (x, 0, i) ) + point ([1,16]) plots.append(p) animate(plots)
#16 @interact def fprime(xcord=(0,20,1)): f(x)=16*x^2 m=(f(xcord)-16)/((xcord)-1) p=plot(f, (x, -10, 10))+plot(point([1,16]))+plot(m*(x-1)+16,ymin=-300, ymax=300) show(p)
#17 @interact def fprime(xcord=(0,20,1)): f(x)=16*x^2 m=(f(xcord)-16)/((xcord)-1) p=plot(f, (x, -10, 10))+plot(point([1,16]))+plot(m*(x-1)+16,ymin=-300, ymax=300)+text(m,[xcord,f(xcord)]) df=diff(f,x) show(p)
#18 @interact def fprime(xcord=(0,20,1)): f(x)=16*x^2 m=(f(xcord)-16)/((xcord)-1) p=plot(f, (x, -10, 10))+plot(point([1,16]))+plot(m*(x-1)+16,ymin=-300, ymax=300)+text(m,[xcord,f(xcord)]) df=diff(f,x) show(p) show(df(1))
Interact: please open in CoCalc
#19 slopes=[] trash=[-2,-1,0.1,2] for t in trash: df=diff(16*x^2,x) s=df.subs(x=t) p=plot(16*x^2, (x, -5,5), ymin=0, ymax=80, color="green")+plot(s*(x-t)+(16*t^2)) slopes.append(p) a=animate(slopes) show(a,gif=true)