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

1.	Evaluate : \(\lim\limits_{x \to 0}\frac{e^x-e^{sinx}}{x-sinx}\)
Answer» \(\lim\limits_{x \to 0}\frac{e^x-e^{sinx}}{x-sinx}\) \(=\lim\limits_{x \to 0}e^{sin\,x}(\frac{e^{x-sinx}-1}{x-sinx})\) \(=\lim\limits_{x \to 0}e^{sin\,x}.\lim\limits_{x \to 0}(\frac{e^{x-sinx}-1}{x-sinx})\) \(=e^{sin0}.1\) = 1

Answer»

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

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

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

\(=e^{sin0}.1\)

= 1

Discussion

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