Evaluate limit, changing the form of the function where necessary. See details below.

Question

lim as x approaches 1. (2x-1)^2-1/(2x-2) ***Pls show all work. Thanks.***

Answer 1

(2x-1)^2 as x gotu 1=(2-1)^2=1^2=1... -1/(2x-2) as x gotu 1=-1/0=-infinity... 1-infinity=-infinity

Answer 2

Given ((2x-1)^2-1)/2x-2

From L'hospital's rule

d((2x-1)^2-1)/dx=4(2x-1)

d(2x-2)/dx=2

dy/dx=4(2x-1)/2

the limit of dy/dx as it approaches 1 is given by

4(2*1-1)/2

=4(2-1)/2

=4/2

=2

There fore the limit of the given function as it approaches 1=2