Lim x - 01-cos 3 x-x3x-1-

The correct option is B x → 0lim1 cos 3x/x(3^x 1) cos 3x=1 9x^2/2!+… 1 cos 3x=9x^2/2!+… ......... (1) x→ 0lim3^x 1/x=log 3 .......... (2) x→ 0lim1 cos 3 ...

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Byju's Answer

Standard XI

Mathematics

Expansions to Remove Indeterminate Form

lim x → 01-co...

Question

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

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Solution

The correct option is 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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Similar questions

{lim}_{x \to 0} \frac{1 - c o s^{3} x}{x s i n x c o t x}

lim x \to 0 \frac{1 - {cos}^{3} x}{x sin 2 x}

${lim}_{x \to 0}$ $\frac{1 - {c o s}^{3} x}{s i n 3 x . s i n 5 x}$ =

lim x \to 0 \frac{1 - {cos}^{3} x}{x sin 2 x}

equals :-

Solve:

{lim}_{x \to 0} \frac{(1 - cos 3 x)}{x sin 2 x}

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limx→01−cos 3xx(3x−1)=

The correct option is B limx→01−cos3xx(3x−1) cos 3x=1−9x22!+… 1−cos 3x=9x22!+… ......... (1) limx→03x−1x=log 3 .......... (2) limx→01−cos 3xx2(3x−1x) From (1) and (2) we get =92 log 3

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