CoCalc -- 2015-09-24-124615.sagews

³⁴ views

var('x y')
y=limit(sin(x)/x,x=0)
show(y)

(x, y)

\displaystyle 1

var('x y')
y=integral(sin(x)+cos(x),x,0,pi/4)
show(y)

(x, y)

\displaystyle 1

var('x y')
y=limit((x+3)/(x-3),x=3,dir='plus')
show(y)

(x, y)

\displaystyle +\infty

var('x y')
y=diff(3*x*sin(x)-cos(x)^2,x)
show(y)

(x, y)

\displaystyle 3 \, x \cos\left(x\right) + 2 \, \cos\left(x\right) \sin\left(x\right) + 3 \, \sin\left(x\right)

var('x y')
y=diff(((e^x)/(x+1))*sin(x),x)
show(y)
show(y(3))

(x, y)

\displaystyle \frac{\cos\left(x\right) e^{x}}{x + 1} + \frac{e^{x} \sin\left(x\right)}{x + 1} - \frac{e^{x} \sin\left(x\right)}{{\left(x + 1\right)}^{2}}

\displaystyle \frac{1}{4} \, \cos\left(3\right) e^{3} + \frac{3}{16} \, e^{3} \sin\left(3\right)

var('x y z')
implicit_plot3d(x^2+y^2-z,(x,-10,10),(y,-10,10),(z,-10,10))

(x, y, z)

3D rendering not yet implemented

var('t')
parametric_plot3d((cos(t),sin(t),t),(-10,10))

t

3D rendering not yet implemented

var('a b c d x s u pt1 pt2 pt3 pt4 t')
a=vector([t,t^2,3*t])

x=diff(a,t)
s=a.norm()
b=(x/s).simplify_full()


c=diff(b,t)
u=c.norm()
d=(c/u).simplify_full()

z=(b.cross_product(d)).simplify_full()

pt1=a(5)
pt2=a(5)+b(5)
pt3=a(5)+d(t=5)
pt4=a(5)+z(t=5)

parametric_plot3d((t,t^2,3*t),(-10,10))+line3d([(pt1),(pt2)])+line3d([(pt1),(pt3)])+line3d([(pt1),(pt4)])

(a, b, c, d, x, s, u, pt1, pt2, pt3, pt4, t)

/projects/sage/sage-6.9/local/lib/python2.7/site-packages/smc_sagews/sage_server.py:905: DeprecationWarning: Substitution using function-call syntax and unnamed arguments is deprecated and will be removed from a future release of Sage; you can use named arguments instead, like EXPR(x=..., y=...)
See http://trac.sagemath.org/5930 for details.
  exec compile(block+'\n', '', 'single') in namespace, locals

3D rendering not yet implemented

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