AP EAMCET · Maths · Limits
\(\lim _{x \rightarrow 0} \frac{x^2 \sin ^2(3 x)+\sin ^4(6 x)}{(1-\cos 3 x)^2}=\)
- A \(\frac{580}{9}\)
- B \(\frac{145}{3}\)
- C \(\frac{580}{3}\)
- D \(\frac{145}{9}\)
Answer & Solution
Correct Answer
(A) \(\frac{580}{9}\)
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow 0} \frac{x^2 \sin ^2(3 x)+\sin ^4(6 x)}{(1-\cos 3 x)^2} = \lim _{x \rightarrow 0} \frac{\left(\frac{\sin (3 x)}{x}\right)^2+\left(\frac{\sin (6 x)}{x}\right)^4}{\left(\frac{1-\cos 3 x}{x^2}\right)^2}\)…
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