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