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#!/usr/bin/env python
"""Limits Example
Demonstrates limits.
"""
from sympy import exp, log, Symbol, Rational, sin, limit, sqrt, oo
def sqrt3(x):
return x**Rational(1, 3)
def show(computed, correct):
print("computed:", computed, "correct:", correct)
def main():
x = Symbol("x")
a = Symbol("a")
h = Symbol("h")
show( limit(sqrt(x**2 - 5*x + 6) - x, x, oo), -Rational(5)/2 )
show( limit(x*(sqrt(x**2 + 1) - x), x, oo), Rational(1)/2 )
show( limit(x - sqrt3(x**3 - 1), x, oo), Rational(0) )
show( limit(log(1 + exp(x))/x, x, -oo), Rational(0) )
show( limit(log(1 + exp(x))/x, x, oo), Rational(1) )
show( limit(sin(3*x)/x, x, 0), Rational(3) )
show( limit(sin(5*x)/sin(2*x), x, 0), Rational(5)/2 )
show( limit(((x - 1)/(x + 1))**x, x, oo), exp(-2))
if __name__ == "__main__":
main()
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