limit of (|x+h|-|x|)/h as h goes to 0 at x=4

Question

why is the answer 1?

Answer 1

observe that we can further simplify (|x+h|-|x|)/h to
(x + h - x)/h
(h)/h
1
rewriting,
lim 1 as h->0 at x = 4 is equal to 1, since the limit of a constant is also equal to that constant.

hope this helps~ :)

Answer 2

thank you, i got it