<s>[INST] Find the constant and limit Here is the limit
$$\lim_{x\rightarrow-2}  \frac{4x^2 + ax + a + 12}{x^2 + x - 2}.$$
a) Find the constant $a$
b) find the limit
I dont think it is solvable because it didn't tell me as $x \rightarrow -2$, $y \rightarrow $?
 [/INST] I think it's saying that if the limit exists, find $a$ and find the limit.
If $x \to -2$ then the denominator $\to 0$, so in order for the limit to exist, then the numerator must also $\to 0$.
$(4x^2 +ax +a+12) \to (16 -2a +a+12) = (28-a)$ therefore $a = 28$
So that expression becomes:
$$\lim_{x \to -2} \frac{4x^2 + 28x +40}{x^2+x-2} = \lim_{x \to -2} \frac{4(x+2)(x+5)}{(x+2)(x-1)} = -4$$
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