AP EAMCET · Maths · Limits
\(\lim _{x \rightarrow 0}(1+3 x)^{\frac{2}{x}}=\)
- A 6
- B \(e^6\)
- C \(e^{-6}\)
- D \(e^{\frac{1}{6}}\)
Answer & Solution
Correct Answer
(B) \(e^6\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} \operatorname{Lim}_{x \rightarrow 0}(1 & +3 x) \frac{2}{x}=\operatorname{Lim}_{x \rightarrow 0}\left((1+3 x)^{\frac{1}{3 x}}\right)^6 \\ =e^6 \quad & \left\{\because \operatorname{Lim}_{x \rightarrow 0}(1+a x)^{\frac{1}{a x}}=e,(a \neq 0)\right\} \end{aligned}\)
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