TS EAMCET · Maths · Limits
If \(\lim _{x \rightarrow 0} \frac{3^{x^3}-\left(1-x^3\right)^{2 / 3}}{x^2 \sin x}=p+\log q\) then \(p q=\)
- A \(\frac{2}{3}\)
- B \(2\)
- C \(3\)
- D \(-2\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
\( \lim _{x \rightarrow 0} \frac{3^{x^3}-\left(1-x^3\right)^{2 / 3}}{x^2 \sin x} = \lim _{x \rightarrow 0} \frac{e^{x^3 \ln 3}-(1-x^3)^{2 / 3}}{x^3} \) \( = \lim _{x \rightarrow 0} \frac{(1+x^3 \ln 3 + O(x^6)) - (1 - \frac{2}{3}x^3 + O(x^6))}{x^3} \)…
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