Question

Does anyone know how to do this?

Answer 1

Explanation:

For a. We must find the lim as x approaches 2 from the right.

We can use direct substitution for the second equation because

• We can direct subsitute since we not dealing with no asymptotes
• We use the second equation because that is when x is greater than or equal to two so we use that because we can determine the limit.

So just subsitue 2 in for x.

`- 6(2) {}^(2) + 2m`

`- 6(4) + 2m`

`2m - 24`

So the limit as x approaches 2 from the right, is 2m-24.

b. We now must find the limit as x approaches 2 from the left,

This time we will use the top equation because since the x values for the top equation is only defined to be less than 2, we can know the behavior as it approaches 2 from the left.

Here we direct subsitue again

`6(2) + m`

`12 + m`

So as x approaches 2 from the left, the limit is 12+m

Here we let

`12 + m = 2m - 24`

`36 = m`

The value is 36 so

m=36