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

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

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

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Since the form is indeterminant

$=\cfrac00$

Method 1: factorization

Method 2: By L hospital rule:

Differentiating numerator and denominator separately: