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Question Number 154390 by liberty last updated on 18/Sep/21

$$\underset{x\to 2}{\lim }\frac{x^2{e}^x-4e^2}{x-2}?$$

Commented by puissant last updated on 18/Sep/21

$$=\underset{x\to 2}{\lim }(2{xe}^x+x^2{e}^x)=4e^2+4e^2=8e^2..$$

Answered by yeti123 last updated on 18/Sep/21

$$\underset{x\to 2}{\lim }\frac{x^2{e}^x-4e^2}{x-2}=\underset{x\to 2}{\lim }\frac{2{xe}^x+x^2{e}^x}{1}$$$$=\underset{x\to 2}{\lim }{e}^x(2x+x^2)$$$$=8e^2$$

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