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Composite Function

Evaluate li...

Question

Evaluate $lim x \to \infty (\frac{x}{e} - {x (\frac{x}{x + 1})}^{x})$

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Solution

$\begin{matrix} {lim}_{x \to \infty} (\frac{x}{e} - x {(\frac{x}{x + 1})}^{x}) = 2 \Rightarrow {lim}_{x - \infty} {(1 + \frac{1}{x})}^{x} = 2 \Rightarrow {lim}_{x \to \infty} (\frac{x}{e} - \frac{x}{e}) = 0 A n s . \end{matrix}$

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