How do you evaluate the limit of $(3x+9)/(x^2-5x-24)$ as $x->2$ ?

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Answer 1 · 2017-01-17T14:42:08

By substitution.

If $x$ is approaching $2$ , then

the numerator is approaching $3(2)+9 = 6+9 = 15$

and the denominator is approaching $(2)^2-5(2)-24 = 4-10-24 = -30$

So the limit of the quotient is $15/(-30) = -1/2$

How do you evaluate the limit of (3x+9)/(x^2-5x-24)(3x+9)/(x^2-5x-24) as x->2x->2?