Hello, qbkr21!

Let and let

Determine each of the following: .

You will notice that the values that you entered are getting closer and closer to a number .

This number is called the limit of as

and is also called the derivative of at the point when

Enter the value of the number ____?_____.

First, we'll determine . . . and do all the algebra first.

There are three stages to

. . (1) Find . . . and simplify.

. . (2) Subtract . . . and simplify.

. . (3) Divide by . . . and simplify.

(1)

. . . . . . . . .

. . . . . . . . .

(2)

Subtract: .

(3) Divide by

. . .Factor and simplify: .

There! . . .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Now we can crank out the answers.

As (gets smaller and smaller), approaches 25.

Andthatit the limit they're asking for: .