Evaluate:\(\lim\limits_{x \to 5}\frac{e^x-e^5}{x-5}\)

1.	Evaluate:\(\lim\limits_{x \to 5}\frac{e^x-e^5}{x-5}\)
Answer» \(\lim\limits_{x \to 5}\frac{e^x-e^5}{x-5}\) \(=\lim\limits_{x \to 0}\frac{e^{n+5}-e^5}{n}\) [Let x – 5 = n ⇒ as x - 5, n → 0] \(=\lim\limits_{x \to 0}\frac{e^5(e^n-1)}{n}\) \(=e^5\lim\limits_{x \to 0}\frac{e^n-1}{n}\) \(=e^5.1 \) \(=e^5\)

Answer»

\(\lim\limits_{x \to 5}\frac{e^x-e^5}{x-5}\)

\(=\lim\limits_{x \to 0}\frac{e^{n+5}-e^5}{n}\) [Let x – 5 = n ⇒ as x - 5, n → 0]

\(=\lim\limits_{x \to 0}\frac{e^5(e^n-1)}{n}\)

\(=e^5\lim\limits_{x \to 0}\frac{e^n-1}{n}\)

\(=e^5.1 \)

\(=e^5\)

Discussion

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