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Question
Evaluat `lim_(x->0) (e^(2x)-(1+x)^2)/(xlog(1+x)`
Sum
Solution
`lim_(x->0) (e^(2x)-(1+x)^2)/((xlog(1+x))/x x)`
`=lim_(x->0) 1.(e^(2x)-(1+x)^2)/(x x)`
`=lim_(x->0) 1.(e^(2x)-(1+x)^2)/x^2`
Applying L-Hospital rule
`lim_(x->0 ) 1.(2e^(2x)-2(1+x)^1)/(2x)`
`=lim_(x->0)1.(4e^(2x)-2)/2`
`=(4e^0-2)/2=1.`
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L‐ Hospital Rule
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