Find all the real numbers a, so that the following limit exists.

L=

Calculate the value of L and a

Step-by-step explanation:

In order for the limit to exist at x=-2, the denominator factor of (x+2) must be canceled by a numerator factor of (x+2). Synthetic division (see below) shows the remainder when the numerator is divided by (x+2) is (15-a). In order for that remainder to be zero, so that (x+2) is a factor, we must have ...

__

The same synthetic division shows the other numerator factor to be ...

  (3x +(a -6))

For a=15, this is ...

  (3x +9)

and the expression becomes ...

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