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Question Number 212405 by mathlove last updated on 13/Oct/24

$$\underset{x\to 3}{\lim }\frac{e^x-e^3}{x-3}=?$$

Answered by som(math1967) last updated on 13/Oct/24

$$\underset{x\to 3}{lim}\frac{e^3(e^{x-3}-1)}{(x-3)}$$$$=e^3\underset{a\to 0}{lim}\frac{e^a-1}{e^a}[letx-3=a$$$$\because x\to 3\therefore (x-3)\to 0\therefore a\to 0]$$$$=e^3\times 1=e^3$$

Commented by mathlove last updated on 13/Oct/24

$$thankssir$$

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