The correct option is A 12/5 lim_x → 4 √(1+6x) 5√(x) 2 =lim_x → 4(1+6x 25)(√(x)+2)(√(1+6x)+5)(x 4) =lim_x → 46(x 4)(√(x)+2)(√(1+6x)+5)(x 4) ...

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Theorems for Differentiability

limx → 4√1+6x...

Question

$l i m_{x \to 4} \frac{\sqrt{1 + 6 x} - 5}{\sqrt{x} - 2}$

12 / 5

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4 / 5

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0

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Solution

The correct option is A $12 / 5$
$l i m_{x \to 4} \frac{\sqrt{1 + 6 x} - 5}{\sqrt{x} - 2}$

$= l i m_{x \to 4} \frac{(1 + 6 x - 25) (\sqrt{x} + 2)}{(\sqrt{1 + 6 x} + 5) (x - 4)}$

$= l i m_{x \to 4} \frac{6 (x - 4) (\sqrt{x} + 2)}{(\sqrt{1 + 6 x} + 5) (x - 4)}$

$= l i m_{x \to 4} \frac{6 (\sqrt{x} + 2)}{\sqrt{1 + 6 x} + 5}$

$= 6 \times \frac{\sqrt{4} + 2}{\sqrt{25} + 5} = \frac{12}{5}$

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