First slide

Introduction to limits

Question

The value of $lim_{x \to - 2} \frac{{(x^{2} - x - 6)}^{2}}{(x + 2)^{2}}$ , is

Moderate

A

6
B

25
C

9
D

16

Solution

We have,
$\begin{array}{l} lim_{x \to - 2} \frac{{(x^{2} - x - 6)}^{2}}{(x + 2)^{2}} \\ = lim_{x \to - 2} \frac{(x - 3)^{2} (x + 2)^{2}}{(x + 2)^{2}} = lim_{x \to - 2} (x - 3)^{2} = (- 2 - 3)^{2} = 25 \end{array}$

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