Step-by-step 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.
[tex] - 6(2) {}^{2} + 2m[/tex]
[tex] - 6(4) + 2m[/tex]
[tex]2m - 24[/tex]
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
[tex]6(2) + m[/tex]
[tex]12 + m[/tex]
So as x approaches 2 from the left, the limit is 12+m
Here we let
[tex]12 + m = 2m - 24[/tex]
[tex]36 = m[/tex]
The value is 36 so
m=36
