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lim(x->0)((1-e^2x)/(1-e^x))

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zainabalaswad | High School Teacher | eNotes Newbie

Posted March 19, 2012 at 3:56 AM via web

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lim(x->0)((1-e^2x)/(1-e^x))

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rcmath | High School Teacher | (Level 1) Associate Educator

Posted March 19, 2012 at 4:11 AM (Answer #1)

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`lim_(x->0)[1-e^(2x)]/[1-e^x]=`

`lim_(x->0)[(1-e^x)(1+e^x)]/(1-e^x)=`

`lim_(x->0)1+e^x=`

`1+1=2`

 

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zainabalaswad | High School Teacher | eNotes Newbie

Posted March 19, 2012 at 4:57 AM (Answer #2)

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otner solution:

By L'Hôpital's rule we get:

lim as x goes to 0 (  -2e^2x / - e^x )  =

lim as x goes to 0 ( 2e^x ) = 2

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