Question

evaluate the limits.​

Answer 1

Answer:

lim (a^x - b^x) /x = ln(a/b) or log(a/b)

x->0

Explanation:

=> (a^x−b^x) /x = (a^x−1) /x − (b^x−1) /x

={a^(0+x)−a^0} /x − {b^(0+x) −b^0} /x

Now

lim (a^x + b^x) /x = [ lim {a^(0+x) - a^0}/x -

x->0. . . . . . . . . . . . . x ->0

lim {b^(0+x) - b^0}/x ] = ln a - ln b =ln(a/b)

x->0

Hope it will help you.....

Answer 2

Answer:

Step-by-step explanation:

solving these by l hospitals rule

differentiating numerator and denominator w r t x

we get

a power x log a - b power x log b

substitute x=0

log a- log b

log (a/b)