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Evaluate lim(hto0) (log(e)(1+2h)-2log(e)...

Evaluate `lim_(hto0) (log_(e)(1+2h)-2log_(e)(1+h))/(h^(2)).`

Text Solution

Verified by Experts

`underset(hto0)lim(log_(e)(1+2h)-2log_(e)(1+h))/(h^(2))`
`=underset(hto0)lim(log_(e)[(1+2h)/(1+2h+h^(2))])/(h^(2))`
`=underset(hto0)lim(log_(e)[1+(-h^(2))/(1+2h+h^(2))])/((-h^(2))/(1+2h+h^(2)))xx(-1)/(1+2h+h^(2))`
`=1xxunderset(hto0)lim(-1)/(1+2h+h^(2))`
`=-1`
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