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What is lim(xto0)(a^(x)-b^(x))/(x)?...

What is `lim_(xto0)(a^(x)-b^(x))/(x)`?

A

`log((a)/(b))`

B

`log((b)/(a))`

C

ab

D

log (ab)

Text Solution

Verified by Experts

The correct Answer is:
A
Let `L=underset(xto0)lim(a^(x)-b^(x))/(x)`
This is of `(0)/(0)` form so, L' hospital' is applicable.
`=L=underset(xto0)lim(a^(x)loga-b^(x)logb)/(1)` (by L' Hospital's rule)
`=loga-logb=log""(a)/(b)`
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