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Evaluate the limit: lim(x->oo)((x+2)/(x+...

Evaluate the limit: `lim_(x->oo)((x+2)/(x+1))^(x+3)`

Text Solution

Verified by Experts

The correct Answer is:
`e`
LetA=`underset(xtooo)lim((x+2)/(x+1))^(x+3)`
`=underset(xtooo)lim(1+(1)/(x+1))^(x+3)`
`=underset(xtooo)lim[(1+(1)/(x+1))^(x+1)]^(((x+3))/((x+1)))`
`=underset(xtooo)lim[(1+(1)/(x+1))^(x+1)]^(underset(xtooo)"lim"(1+(3)/(x))/(1+(1)/(x)))`
`=e^(1)`
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