limx→01−cos 3xx(3x−1)=

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Question

$l i m x \to 0 \frac{1 - c o s 3 x}{x (3^{x} - 1)} =$

Options:

A .

\frac{9}{2}

B .

\frac{9}{(2 log 3)}

C .

\frac{9 log 3}{2}

D .

1

Answer: Option B
:
B

lim x \to 0 \frac{1 - cos 3 x}{x (3^{x} - 1)}

c o s 3 x = 1 - \frac{9 x^{2}}{2!} + \dots

1 - c o s 3 x = \frac{9 x^{2}}{2!} + \dots

......... (1)

l i m x \to 0 \frac{3^{x} - 1}{x} = l o g 3

.......... (2)

l i m x \to 0 \frac{1 - c o s 3 x}{x^{2} (\frac{3^{x} - 1}{x})}

From (1) and (2) we get

= \frac{9}{2 l o g 3}

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