First slide

Introduction to limits

Question

Let $f (x) = \frac{1}{\sqrt{18 - x^{2}}}$ The value of $lim_{x \to 3} \frac{f (x) - f (3)}{x - 3}$ , is

Moderate

A

0
B

$- 1 / 9$
C

$- 1 / 3$
D

$1 / 9$

Solution

We have,
$lim_{x \to 3} \frac{f (x) - f (3)}{x - 3} = f^{'} (3)$
Now, $f^{'} (x) = \frac{x}{{(18 - x^{2})}^{3 / 2}} \Rightarrow f^{'} (3) = \frac{3}{(9)^{3 / 2}} = \frac{1}{9}$

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