# Evaluate the following limit : lim(x→-2) (x^3 + x^2 + 4x + 12)/(x^3 - 3x + 2)

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Evaluate the following limit : $\lim\limits_{\text x \to -2}\cfrac{\text x^3+\text x^2+4\text x+12}{\text x^3-3\text x+2}$

lim(x→-2) (x3 + x2 + 4x + 12)/(x3 - 3x + 2)

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Since the form is

$=\cfrac00$

Method 1: factorization

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

Method 2: By L hospital rule:

Differentiating numerator and denominator separately: