First slide

Introduction to limits

Question

Let $f (2) = 4 and f^{'} (2) = 4$ Then, $lim_{x \to 2} \frac{x f (2) - 2 f (x)}{x - 2}$ is given by

Moderate

A

2
B

-2
C

-4
D

3

Solution

We have,
$\begin{array}{l} lim_{x \to 2} \frac{x f (2) - 2 f (x)}{x - 2} \\ = lim_{x \to 2} \frac{x f (2) - 2 f (2) + 2 f (2) - 2 f (x)}{x - 2} \\ = lim_{x \to 2} \frac{(x - 2) f (2)}{x - 2} - 2 lim_{x \to 2} \frac{f (x) - f (2)}{x - 2} \\ = f (2) - 2 f^{'} (2) = 4 - 2 \times 4 = - 4 \end{array}$

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