Question Number 30511 by abdo imad last updated on 22/Feb/18
![find lim_(x→+∞) e^x [(1/x)].](https://www.tinkutara.com/question/Q30511.png)
$${find}\:\:{lim}_{{x}\rightarrow+\infty} \:\:{e}^{{x}} \:\left[\frac{\mathrm{1}}{{x}}\right]. \\ $$
Commented by abdo imad last updated on 24/Feb/18
![for x>1 ⇒ 0<(1/x)<1 ⇒ [(1/x)]=0 ⇒ ∀x>1 e^x [(1/x)]=0⇒ lim_(x→+∞) e^x [(1/x)]=0 so the function [..] defeat e^x .](https://www.tinkutara.com/question/Q30705.png)
$${for}\:{x}>\mathrm{1}\:\Rightarrow\:\mathrm{0}<\frac{\mathrm{1}}{{x}}<\mathrm{1}\:\Rightarrow\:\left[\frac{\mathrm{1}}{{x}}\right]=\mathrm{0}\:\Rightarrow\:\forall{x}>\mathrm{1}\:{e}^{{x}} \:\left[\frac{\mathrm{1}}{{x}}\right]=\mathrm{0}\Rightarrow \\ $$$${lim}_{{x}\rightarrow+\infty} {e}^{{x}} \left[\frac{\mathrm{1}}{{x}}\right]=\mathrm{0}\:{so}\:{the}\:{function}\:\left[..\right]\:{defeat}\:{e}^{{x}} \:. \\ $$