lim _x arrow 0 frac2 sin^2 3 xx^2 is equal to

Correct answer: (B) 18. Consider lim _x arrow 0 frac2 sin^2 3 xx^2 =2 · lim _x arrow 0 [(sin 3 x)/x ]^2=2 · lim _x arrow 0 [3 (sin 3 x)/(3 x) ]^2 =2.9 lim _x arrow 0 ((sin 3 x)/(3 x) )^2=18 × 1=18

Q73 / 125 · BITSAT 2021 · Mathematics

$\lim _{x \rightarrow 0} \frac{2 \sin ^{2} 3 x}{x^{2}}$ is equal to

A
12
Correct answer
B
18
C
0
D
6

Solution

Consider $\lim _{x \rightarrow 0} \frac{2 \sin ^{2} 3 x}{x^{2}}$ $\begin{array}{l} =2 \cdot \lim _{x \rightarrow 0}\left[\frac{\sin 3 x}{x}\right]^{2}=2 \cdot \lim _{x \rightarrow 0}\left[3 \frac{\sin 3 x}{3 x}\right]^{2} \\ =2.9 \lim _{x \rightarrow 0}\left(\frac{\sin 3 x}{3 x}\right)^{2}=18 \times 1=18 \end{array}$

Hence, the correct answer is option: 'B'.

$\lim _{x \rightarrow 0} \frac{2 \sin ^{2} 3 x}{x^{2}}$ is equal to

Solution

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