Question

(a^x - b^x)/x as x tends to 0

Answer 1

Sol. As we have,
Lim x → 0 (a^x-b^x)/x

Now adding and subtracting 1

So, Lim x → 0 (a^x-b^x+1-1)/x

or Lim x → 0 [(a^x-1)-(b^x-1)]/x

Now using Lim x → 0 (a^x-1)/x = log a

So, we have Lim x → 0 (a^x-1)/x - Lim x → 0 (b^x-1)/x

 = log a - log b
or log (a/b)