Evaluate lim(x→0)(e^x-e^sinx)/x-sinx

Question

Evaluate : \(\lim\limits_{x \to 0}\frac{e^x-e^{sinx}}{x-sinx}\)

Answer 1

\(\lim\limits_{x \to 0}\frac{e^x-e^{sinx}}{x-sinx}\) 

\(=\lim\limits_{x \to 0}e^{sin\,x}(\frac{e^{x-sinx}-1}{x-sinx})\) 

\(=\lim\limits_{x \to 0}e^{sin\,x}.\lim\limits_{x \to 0}(\frac{e^{x-sinx}-1}{x-sinx})\) 

\(=e^{sin0}.1\) 

= 1

Comments

good answer