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lim-x-sinx-pi-2-x-




Question Number 195192 by mustafazaheen last updated on 26/Jul/23
  lim_(x→∞) (sinx+(π/2))^x =?
$$ \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{sinx}+\frac{\pi}{\mathrm{2}}\right)^{\mathrm{x}} =? \\ $$
Answered by MM42 last updated on 26/Jul/23
sinx+(π/2)>1  ⇒lim_(x→+∞)  =+∞  &   lim_(x→−∞) =0
$${sinx}+\frac{\pi}{\mathrm{2}}>\mathrm{1} \\ $$$$\Rightarrow{lim}_{{x}\rightarrow+\infty} \:=+\infty\:\:\&\:\:\:{lim}_{{x}\rightarrow−\infty} =\mathrm{0} \\ $$

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