Question Number 49802 by maxmathsup by imad last updated on 10/Dec/18
$${find}\:{lim}_{{x}\rightarrow{e}} \:\:\:\frac{{e}^{{x}} \:−{e}^{{e}} }{{x}^{{e}} \:−{e}^{{e}} } \\ $$
Answered by tanmay.chaudhury50@gmail.com last updated on 11/Dec/18
$${li}\underset{{x}\rightarrow{e}} {{m}}\:\:\frac{{e}^{{x}} }{{ex}^{{e}−\mathrm{1}} } \\ $$$$=\frac{{e}^{{e}} }{{e}×{e}^{{e}−\mathrm{1}} }=\frac{{e}^{{e}} }{{e}^{{e}} }=\mathrm{1} \\ $$$${using}\:{L}\:{Hospitsl} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\underset{{t}\rightarrow\mathrm{0}} {\mathrm{li}} \\ $$