Quandaries and Queries


Circe Vera

Calculus AP (High School)

I'm a student, and this is my homework.

Lim 3x 3+ax+a+3 /(x 2+x-2), X->-2



Hi Circe,

The first fact that I noticed is that when x = -2, the denominator is zero. That is

(-2) 2 + (-2) - 2
= 4 -2 -2 = 0
Thus, if the numerator is not zero then the limit does not exist.

What value of a makes the numerator equal to zero?

When a has this value the numerator has a root of x = -2 and hence (x + 2) is a factor of the numerator.

Does this help?

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