Answer:
4x
Step-by-step explanation:
lim 2(x+h)^2 +4 - (2x^2 +4)
-------------------------------------
h
FOIL the (x+h)^2 x^2 +xh+xh+h^2 = x^2 +2xh+h^2 and substitute in
lim 2(x^2 +2xh +h^2) +4 - (x^2 +4)
-------------------------------------
h
Distribute the 2 and the negative sign
lim 2x^2 +4xh +2h^2 +4 - 2x^2 -4
-------------------------------------
h
Combine like terms (the 2x^2 and the 4 go away)
lim +4xh +2h^2
-------------------------------------
h
Factor out an h from the numerator
lim h(4x +2h)
-------------------------------------
h
Cancel the h from the top and bottom
lim +4x +2h
The limit as h goes to 0, means we let h be 0
lim 4x +0
lim is 4x
