#### To determine

**To state: **

Whether the given statement, "If
g(x)=
x
5
, then
lim
x→2
g(x)−g(2)
x−2
=80
" is true of false.

#### Answer

The given statement is true.

#### Explanation

gx=x5

Now we have to find limx→2gx-g(2)x-2, by definition this is the derivative of

gx=x5 at x =2.

That is, g'2=limx→2 gx-g(2)x-2

So we just find g'2 by using power function rule, ddxxn=nxn-1

gx=x5⇒g'x=5x4

⇒g'2=5*24=5*16=80

Hence, the statement is true.

**Final statement:**

The given statement is true.