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Lim X → 0 Sin 2 4 X 2 X 4 - Mathematics

\[\lim_{x \to 0} \frac{\sin^2 4 x^2}{x^4}\] 

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Solution

\[\lim_{x \to 0} \left[ \frac{\sin^2 4 x^2}{x^4} \right]\] 

\[= \lim_{x \to 0} \left[ \frac{\sin\left( 4 x^2 \right)}{x^2} \times \frac{\sin\left( 4 x^2 \right)}{x^2} \right]\]
\[ = \lim_{x \to 0} \left[ \frac{\sin\left( 4 x^2 \right)}{4 x^2} \times 4 \times \frac{\sin\left( 4 x^2 \right)}{4 x^2} \times 4 \right]\]
\[ = 4 \times 4 \left[ \because \lim_{x \to 0} \frac{\sin x}{x} = 1 \right]\]
\[ = 16\] 

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 29 Limits
Exercise 29.7 | Q 18 | Page 50
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