Question

show that limit of log(2x-3)/2(x-2)=1 as x approaches to 2?

Answer 1

here is ur answer........

Answer 2

By applying L hosp rule

Differentiate numerator as well as denominator ,

Therefore

Lim

X tends to 2

D/DX [log(2x-3)] / D/ DX 2(x-2)

Lim

X tends to 2

(1/2x-3)×2/ 2(1)

Lim

X tends to 2

(1/2x-3)

Now putting X tends to 2 ,

1/1

=1 proved.

Thankyou I hope it will help.