Answer:
As we get closer to x=-3, the limit is approaches -1, on both sides of -3 so this is a good limit so c is 8.
Step-by-step explanation:
In order for a limit to exists, the left side limit must exist and right side limit must exist and on top of that, they must be equal to each other.
In this case, this a piece wise function and by definition of a limit that exist, the limit of this piece wise function as x approaches 3 from either side, must be equal.
We let x=-3 for the top equation.
[tex]( - 3) {}^{2} - 10 = - 1[/tex]
So we set the second equation equal to -1.
[tex] - ( {x}^{2} ) + c = - 1[/tex]
[tex] - ( - 3 {}^{2} ) + c = - 1[/tex]
[tex] - 9 + c = - 1[/tex]
[tex]c = 8[/tex]
So the value of c is 8. We can prove this by graphing as well.
