Question

lim -2 ((3x^2)+ax+a+3)/((x^2)+x-2)

Answer 1

Is it
\[\lim_{x \rightarrow (-2)}\frac{ 3x^2 + ax+ a + 3 }{ x^2 + x - 2 }\]
??

Answer 2

Yes it is. I need to find the value of a

Answer 3

Does the question tells anything about the value of the limit ??

Answer 4

There is a number 'a' such that lim -2 ((3x^2)+ax+a+3)/((x^2)+x-2) exists. Find the value of 'a' and then the limit value.

Answer 5

Okay..I understood the question.

Answer 6

Can you tell me why the limit does not exist for all real values of 'a' ??

Answer 7

@star2595 ??

Answer 8

I'm not sure :/

Answer 9

Do you know L' Hospital's Rule ?
http://en.wikipedia.org/wiki/L%27H%C3%B4pital%27s_rule

Answer 10

No, first time seeing it.

Answer 11

How do you generally solve limits ??

Answer 12

The only other piece of information given is "Think about the indeterminate form that usually gives rise to a nice value"
It's a question we never went over yet so its more of a challenge problem on the assignment

Answer 13

Okay..so here's the deal.
If we simply put x = (-2) the denominator will become zero.
In order to get the indeterminate form; the numerator should also become zero.

Can you now gimme the value of 'a' ??

Answer 14

15?

Answer 15

Correct :)

Answer 16

Thank you for your help! :)

Answer 17

You're welcome :)