JEE Mains · Maths · STD 11 - 12. limits
\(\lim _{x \rightarrow 0^{+}} \frac{\tan \left(5(x)^{\frac{1}{3}}\right) \log _e\left(1+3 x^2\right)}{\left(\tan ^{-1} 3 \sqrt{x}\right)^2\left(e^{5(x)^{\frac{4}{3}}}-1\right)}\) is equal to
- A \(\frac{1}{15}\)
- B 1
- C \(\frac{1}{3}\)
- D \(\frac{5}{3}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{3}\)
Step-by-step Solution
Detailed explanation
\lim _{x \rightarrow 0^{\cdot}}\left(\frac{\tan \left(5 \mathrm{x}^{1 / 3}\right)}{5 \mathrm{x}^{1 / 3}}\right) \cdot\left(\frac{(3 \sqrt{\mathrm{x}})^2}{\left(\tan ^{-1} 3 \sqrt{\mathrm{x}}\right)^2}\right)\left(\frac{\ell\left(1+3 \mathrm{x}^2\right)}{3…
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