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Evaluate lim(xtoa) (logx-loga)/(x-a)....

Evaluate `lim_(xtoa) (logx-loga)/(x-a).`

Text Solution

Verified by Experts

Let `x-a=h.` Then if `xtoa, hto0.` Therefore,
`underset(xtoa)lim(logx-loga)/(x-a)" "`(0/0 form)
`underset(hto0)lim(log(a+h)-loga)/(h)`
`underset(hto0)lim(log(1+(h)/(a)))/((h)/(a)a)=(1)/(a)`
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