Question

$$
\lim _{x \rightarrow 0+}\left(e^{x}+x\right)^{y / x}
$$
(A) Does not exist finitely (B) is 1
(C) is \(\mathrm{e}^{2}\)
(D) is 2

Answer 1

Ans: (C)
Hint : \(\operatorname{lit}_{x \rightarrow 0^{+}}\left(e^{x}+x\right)^{\frac{1}{x}}=e^{\operatorname{lt} t+0^{+}} \frac{e^{x}+x-1}{x}=e^{\operatorname{lt} t-0^{+}}\left(\frac{e^{x}-1}{x}+1\right)=e^{2}\)