lim4x-1x->1/42x1/2- 1

lim                 4x-1/2x^1/2-1

x-->1/4

4x-1 can be written as (2x^1/2 )² -1²                                   [a²-b²=(a-b)(a+b)]

                               =(2x^1/2-1)(2x^1/2+1)

now we have

lim x-->1/4  (2x^1/2-1)(2x^1/2+1)/(2x^1/2-1)

lim x-->1/4  (2x^1/2+1)

taking limit we get

 limit = 2 ans

Approved