TS EAMCET · Maths · Limits
\(\lim _{x \rightarrow 0} \frac{\tan ^3 x-\sin ^3 x}{x^5}\) is equal to
- A \(\frac{5}{2}\)
- B \(\frac{3}{2}\)
- C \(\frac{3}{5}\)
- D \(\frac{2}{5}\)
Answer & Solution
Correct Answer
(B) \(\frac{3}{2}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \lim _{x \rightarrow 0} \frac{\tan ^3 x-\sin ^3 x}{x^5} \\ & =\lim _{x \rightarrow 0} \frac{\left[\begin{array}{c}\left(x+\frac{x^3}{3}+\frac{2}{15} x^5+\ldots\right)^3 \\ -\left(x-\frac{x^3}{3 !}+\frac{x^5}{5 !}+\ldots\right)^3\end{array}\right]}{x^5} \\ &…
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