Question

Solve
Limit(x-1)
(x^3-3x+1)/(x-1)

Answer 1

apply  le hospital rule as it tends to infinity by putting x = 1 ther for taking derivative of abov and below individual 

we get 3x^2-3/1
now put lmits x tends to 1 therfor ans is 3*1^2-3=0

Answer 2

Limit does not exist, because as x→1-, the expression is positive.
And as x→1+, the expression is negative.
Apply L'Hospital's rule only when the function is in indeterminate form such as $\frac{0}{0}$ or $\frac{\± \infty }{\± \infty}$.