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Question Number 49802 by maxmathsup by imad last updated on 10/Dec/18

find lim_(x→e)    ((e^x  −e^e )/(x^e  −e^e ))

$${find}\:{lim}_{{x}\rightarrow{e}} \:\:\:\frac{{e}^{{x}} \:−{e}^{{e}} }{{x}^{{e}} \:−{e}^{{e}} } \\ $$

Answered by tanmay.chaudhury50@gmail.com last updated on 11/Dec/18

lim_(x→e)   (e^x /(ex^(e−1) ))  =(e^e /(e×e^(e−1) ))=(e^e /e^e )=1  using L Hospitsl            li_(t→0)

$${li}\underset{{x}\rightarrow{e}} {{m}}\:\:\frac{{e}^{{x}} }{{ex}^{{e}−\mathrm{1}} } \\ $$$$=\frac{{e}^{{e}} }{{e}×{e}^{{e}−\mathrm{1}} }=\frac{{e}^{{e}} }{{e}^{{e}} }=\mathrm{1} \\ $$$${using}\:{L}\:{Hospitsl} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\underset{{t}\rightarrow\mathrm{0}} {\mathrm{li}} \\ $$

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