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

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

Discussion

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