Evaluate _ x 1 [ (1+x)- 2 x 3 4^ x-1 -3 x ] (7+x)^ 1 / 3 -(1+3 x)^ 1 / 2 x . .
Mathematics · JEE Main · NTA Exams — Limit, Continuity and Differentiability
Evaluate \(\lim _{x \rightarrow 1} \frac{\left[\log (1+x)-\log 2 x 3 \cdot 4^{x-1}-3 x\right]}{\left\{(7+x)^{1 / 3}-(1+3 x)^{1 / 2} \sin \pi x\right.}\).
- \(\frac{4}{\pi} \log e\)
- \(\frac{9}{\pi} \log \frac{4}{e}\)
- \(\frac{8}{\pi} \log \frac{e}{4}\)
- none of these
Answer
(B) 9 4 e
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