examples/limits_examples.py

   1 #!/usr/bin/env python
   2 import iam_sympy_example
   3
   4 from sympy import exp,log,Symbol,Rational,sin,limit, sqrt,oo
   5
   6 x=Symbol("x")
   7 a=Symbol("a")
   8 h=Symbol("h")
   9
  10 def sqrt3(x):
  11     return x**Rational(1,3)
  12
  13 def show(computed, correct):
  14     print "computed:",computed,"correct:",correct
  15
  16 show( limit(sqrt(x**2-5*x+6)-x,x,oo) , -Rational(5)/2 )
  17 #show( limit(x*(sqrt(x**2+1)-x),x,oo) , Rational(1)/2 )
  18 show( limit(x-sqrt3(x**3-1),x,oo) , Rational(0) )
  19 show( limit(log(1+exp(x))/x,x,-oo) , Rational(0) )
  20 show( limit(log(1+exp(x))/x,x,oo) , Rational(1) )
  21 show( limit(sin(3*x)/x,x,0) , Rational(3) )
  22 show( limit(sin(5*x)/sin(2*x),x,0) , Rational(5)/2 )
  23 #show( limit(((x-1)/(x+1))**x,x,oo) , exp(-2))