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

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Answer 1 · 2017-01-17T14:42:08

By substitution.

If $x$ $x$ is approaching $2$ $2$ , then

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

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

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

How do you evaluate the limit of (3x+9)/(x^2-5x-24)3x+9x2−5x−24(3x+9)/(x^2-5x-24) as x->2x→2x->2?