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Question: Let f <sup>¢</sup>(x) = \(\frac{1}{\sqrt{18 - x^{2}}}\), the value of \(\underset{x \rightarrow 3}{L...

Let f ¢(x) = 118−x2\frac{1}{\sqrt{18 - x^{2}}}, the value of Limx→3(f(x)−f(3)x−3)\underset{x \rightarrow 3}{Lim}\left( \frac{f(x) - f(3)}{x - 3} \right) is

A

0

B

–1/9

C

+1/3

D

1/9

Answer

+1/3

Explanation

Solution

Limx→3f(x)−f(3)x−3\underset{x \rightarrow 3}{Lim}\frac{f(x) - f(3)}{x - 3} Apply L-Hospital rule

Limx→3f′(x)−01\underset{x \rightarrow 3}{Lim}\frac{f'(x) - 0}{1} = f ¢(3) = 118−9\frac{1}{\sqrt{18 - 9}} = 19\frac{1}{\sqrt{9}} = 13\frac{1}{3}