L'hospital Rule And Differntiation

 L'Hospital Rule

from sympy import *

x, y = symbols('x y') 

n=(x ** 2 - 1)

d=(x ** 2 - x)

expr = n/d 

print("Expression f(x): {}\nlimit f(x) x->0 = {}".format(expr,limit(expr,x,0))) 

 

expr_diff = Derivative(expr, x).doit()  

print("f'(x)=",expr_diff) 

expr_diff = Derivative(expr_diff, x).doit() 

print("f''(x)=",expr_diff) 

r=t/k

print(r)

print("limit f(x) x->0 =",limit(r,x,0))