AP EAMCET · Maths · Limits
\(\lim _{x \rightarrow 0} \frac{x^2(\tan 2 x-2 \tan x)^2}{(1-\cos 2 x)^4}=\)
- A 4
- B 2
- C \(\frac{1}{2}\)
- D \(\frac{1}{4}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{4}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & =\lim _{x \rightarrow 0} \frac{4 x^8\left[\left(\frac{4}{3}-\frac{1}{3}\right)+\frac{2}{15}\left(16 x^2-x^2\right)+\ldots\right]^2}{16 x^8\left[1+\frac{x^2}{3}+\ldots\right]^4} \\ & =\frac{4}{16}=\frac{1}{4}\end{aligned}\)
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