If f(9) = 9, f'(9) = 4, then lim x → 9 √ f ( x ) − 3 √ x − 3 equals Options: A . &nbsp 2 B . &nbsp 4 C . &nbsp 6 D . &nbsp 0

Answer: Option B : B Given that f(9) = 9, f’(9) = 4 l i m x → 9 √ f ( x ) − 3 √ x − 3 On rationalisation we get - = l i m x → 9 ( √ f ( x ) − 3 √ x − 3 ) ( √ x + 3 √ x + 3 ) ( √ f ( x ) + 3 √ f ( x ) + 3 ) = l i m x → 9 f ( x ) − f ( 9 ) x − 9 . 6 6 = l i m x → 9 f ( x ) − f ( 9 ) x − 9 = f ′ ( 9 ) = 4

If f(9) = 9, f'(9) = 4, then limx→9√f(x)−3√x&

Discussion Forum : Limits Continuity And Differentiability

Question -

If f(9) = 9, f'(9) = 4, then $lim x \to 9 \frac{\sqrt{f (x)} - 3}{\sqrt{x} - 3}$ equals

Options:

A .

2

B .

4

C .

6

D .

0

Answer: Option B
:
B
Given that f(9) = 9, f’(9) = 4

l i m x \to 9 \frac{\sqrt{f (x)} - 3}{\sqrt{x} - 3}

On rationalisation we get -

= l i m x \to 9 (\frac{\sqrt{f (x)} - 3}{\sqrt{x} - 3}) (\frac{\sqrt{x} + 3}{\sqrt{x} + 3}) (\frac{\sqrt{f (x)} + 3}{\sqrt{f (x)} + 3})

= l i m x \to 9 \frac{f (x) - f (9)}{x - 9}

\frac{6}{6}

= l i m x \to 9 \frac{f (x) - f (9)}{x - 9}

= f^{^{'}} (9)

= 4

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Discussion Forum : Limits Continuity And Differentiability

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