Tính \(\lim\limits_{x\rightarrow0}\left(1+\sin x\right)^{\frac{1}{x}}\).
e \(\frac{1}{e}\) 1 \(\sqrt{e}\) Hướng dẫn giải:\(\lim\limits_{x\rightarrow0}\left(1+\sin x\right)^{\frac{1}{x}}=\lim\limits_{x\rightarrow0}\left[\left(1-2\sin x\right)^{\frac{1}{\sin x}}\right]^{-\frac{\sin x}{x}}=e^1=e\)