Question

can someone help explain how you find the limit of this? thanks

lim as x approaches 1+

((sqrt 2x)(x-1))/(abs x-1)

then lim as x approaches 1-

Answer 1

In case that ^^ wasn't clear enough, I've attached an image of the problem

Answer 2

for part A when approaching from the right
\[|x-1| = x-1\]
so that they cancel, leaving a limit of sqrt(2)

for part B, x being less than 1 you have
\[|x-1| = -(x-1)\]
after cancelling you left with limit of -sqrt(2)

Answer 3

Well, that was embarrassingly simple. Thank you!