lim-x-x-e-sinx-x-

Question Number 101026 by 175 last updated on 29/Jun/20

\lim_{x \to \infty} \frac{x}{e^{\sin x - x}}

Answered by mathmax by abdo last updated on 29/Jun/20

f (x) = \frac{x}{e^{sinx - x}} = x e^{x} e^{- sinx} \Rightarrow \lim_{x \to + \infty} f (x) = \lim_{x \to + \infty} {xe}^{x} = + \infty

and \lim_{x \to - \infty} f (x) = \lim_{x \to - \infty} {xe}^{- x} = 0