First slide

Introduction to limits

Question

If $f (9) = 9, f^{1} (9) = 4, \underset{x \to 9}{L i m} \frac{\sqrt{f (x)} - 3}{\sqrt{x} - 3} =$

Moderate

A

4
B

$\frac{1}{4}$
C

$\frac{1}{2}$
D

$- \frac{1}{2}$

Solution

limit value is 0/0 use L hospital rule
$\underset{x \to 9}{^{\lim}} \frac{\frac{1}{2 \sqrt{f (x)}} . f^{'} (x)}{\frac{1}{2 \sqrt{x}}} = \frac{f' (9)}{\sqrt{f (9)}} \times \sqrt{9} = \frac{4}{3} \times 3 = 4$

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