Question

use the limit laws and theorem to find the limit. a. lim x→3 (x² + 3x)/(x² - x - 2) x² + 3x/x² - x - 2

Explanation:

Step1: Factor the polynomials

First, factor the numerator $x^{2}+3x - 2$ and denominator $x^{2}-x - 2$. The denominator $x^{2}-x - 2=(x - 2)(x+1)$. The numerator $x^{2}+3x - 2$ cannot be factored easily over the integers. But we are finding the limit as $x
ightarrow3$.

Step2: Substitute $x = 3$

Substitute $x = 3$ into the function $\frac{x^{2}+3x - 2}{x^{2}-x - 2}$. We get $\frac{3^{2}+3\times3 - 2}{3^{2}-3 - 2}=\frac{9 + 9-2}{9 - 3-2}=\frac{16}{4}=4$.

Answer:

$4$