WBJEE · Maths · Limits
\(\lim _{x \rightarrow 0^{+}}\left(e^{x}+x\right)^{1 / x}\)
- A Does not exist finitely
- B is 1
- C is \(e^{2}\)
- D is 2
Answer & Solution
Correct Answer
(C) is \(e^{2}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} &\text { Let } L=\lim _{x \rightarrow 0^{+}}\left(e^{x}+x\right)^{1 / x}\\ &\Rightarrow \log L=\lim _{x \rightarrow 0^{+}} \frac{\log \left(e^{x}+x\right)}{x}\\ &\Rightarrow \log L=\lim _{x \rightarrow 0^{+}} \frac{\frac{1}{\left(e^{x}+x\right)} \cdot…
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