Question

Multiple choice find lim 10 points

Answer 1

Aha here is a trick. If you notice, this is the derivative of 2x^2+4. You can use the definition of the derivative to check it. The derivative of 2x^2 + 4, well the 4 goes away and the x^2 becomes 2x, times two which os 4x.

Answer 2

4x

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