Question

Calculati : lim x tinde catre infinit din 2+e la puterea x totul supra x...va rog ajutați-ma este urgent

Answer 1

$\lim_{x\to+\infty}\dfrac{2+e^x}{x}=\lim_{x\to+\infty}\dfrac{2}{x}+\lim_{x\to+\infty}\dfrac{e^x}{x}=\\\\=0+\underbrace{\lim_{x\to+\infty}\dfrac{(e^x)^{'}}{(x)^{'}}}_{Regula\;lui\;L'Hospital}=\lim_{x\to+\infty}\dfrac{e^x}{1}=+\infty.$

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