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BITSAT 2021

Exam: BITSAT
Year: 2021
Subject: Mathematics
Chapter: Limits

BITSAT 2021 · Mathematics · Limits

_ x arrow 0 2 ^ 2 3 x x^ 2 is equal to

\lim _{x \rightarrow 0} \frac{2 \sin ^{2} 3 x}{x^{2}}

is equal to

Options

A12
B18
C0
D6

Correct answer

B. 18

Step-by-step 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}

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