# Evaluate the following limit : lim(x→1)(x^3 + 3x^2-6x + 2)/(x^3 + 3x^2 - 3x - 1)

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Evaluate the following limit : $\lim\limits_{\text x \to 1}\cfrac{\text x^3+3\text x^2-6\text x+2}{\text x^3+3\text x^2-3\text x-1}$

lim(x→1)(x3 + 3x2- 6x + 2)/(x3 + 3x2 - 3x - 1)

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Since the form is

$=\cfrac00$

Method 1: factorization

Since a3 - b3 = (a - b) (a2 + b2 + ab) & a- b2 = (a + b) (a - b)

Method 2: By L hospital rule:

Differentiating numerator and denominator separately: