1830.sagews

circle((1,1),1)

diff(sin(x^2), x, 4)

16*x^4*sin(x^2) - 48*x^2*cos(x^2) - 12*sin(x^2)

integral(x*sin(x^2), x)

-1/2*cos(x^2)

integral(x/(x^2+1), x, 0, 1)

1/2*log(2)

C1 = circle((0,0),3, rgbcolor=(1,1,0))

C2 = circle((0,0),1, rgbcolor=(0,1,1),fill=True)

C3 = circle((0,0),3, rgbcolor=(1,0,1))

show(C1+C2)

C3.show(aspect_ratio=1)

show(C1)

show(C2)

plot(x^2+3,(x,-2,2))

plot(x^2+3,(x,-4,4))

plot(x^2+3,(x,-10,10))

plot(x^2+3,(x,-100,100))

plot(sqrt(8-2*x^2),(x,-5,5))

verbose 0 (3495: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 120 points. verbose 0 (3495: plot.py, generate_plot_points) Last error message: ''

plot(sin(50*x),(x,-2*pi,2*pi),rgbcolor=(0.5,0,1))

plot(sin(50*x),(x,-1,1),rgbcolor=(0.5,0,1))

plot(sin(50*x),(x,-0.1,0.1),rgbcolor=(0.5,0,1))

plot(sin(x)+(1/100)*cos(100*x),(x,-1,1),rgbcolor=(0.5,0,1))

plot(sin(x)+(1/100)*cos(100*x),(x,-0.1,0.1),rgbcolor=(0.5,0,1))

t=var('t')
parametric_plot((t+cos(t),1-sin(t)),(t,0,4*pi),rgbcolor=hue(0.6))

t=var('t')
p1=parametric_plot((cos(t),sin(t)),(t,0,2*pi),rgbcolor=hue(0.2))
p2=parametric_plot((cos(t),sin(t)^2),(t,0,2*pi),rgbcolor=hue(0.4))
p3=parametric_plot((cos(t),sin(t)^3),(t,0,2*pi),rgbcolor=hue(0.6))

show(p1+p2+p3,axes=true)

show(p1+p2+p3,aspect_ratio=1)

show(p1+p2+p3,axes=false,aspect_ratio=1)

g1=plot(sin(x),(x,-pi/2,pi/2),rgbcolor=(0.5,0,1))
g2=plot(arcsin(x),(x,-10,10),rgbcolor=(0.5,0,1))
show(g1+g2)

verbose 0 (3495: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 180 points. verbose 0 (3495: plot.py, generate_plot_points) Last error message: ''

f1=plot(cos(x),(x,0,pi))
f2=plot(arccos(x),(x,-2,2))
show(f1+f2)

verbose 0 (3495: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 100 points. verbose 0 (3495: plot.py, generate_plot_points) Last error message: ''

plot(x*sin(1/x),(x,-2*pi,2*pi),rgbcolor=(0.5,0,1))

plot(sec(x),(x,-1,1))

f = 1/((1+x)*(x-1))
f.partial_fraction(x)

1/2/(x - 1) - 1/2/(x + 1)

def is_even(n):return n%2 == 0

is_even(293)

False

is_even(22)

True

def is_divisible_by(number, divisor=2):return number%divisor == 0

is_divisible_by(6,7)

False

is_divisible_by(20394,7)

False

limit(sin(x)/x,x=0)

1

limit(x^3+ cos(5*x)/10000,x=0)

1/10000

limit(sin(pi/x)/x,x=0)

und

Pi

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_6.py", line 9, in <module> exec compile(ur'open("___code___.py","w").write("# -*- coding: utf-8 -*-\n" + _support_.preparse_worksheet_cell(base64.b64decode("UGk="),globals())+"\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single') File "", line 1, in <module> File "/tmp/tmpQqTeFO/___code___.py", line 2, in <module> exec compile(ur'Pi' + '\n', '', 'single') File "", line 1, in <module> NameError: name 'Pi' is not defined