Question

the initial substitution of x = a yields the form $\frac{0}{0}$. simplify the function algebraically, or use a table or graph to determine the limit. if necessary, state that the limit does not exist. $lim_{x \to 2}\frac{2x^{2}+7x - 22}{x^{2}-4}$. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. $lim_{x \to 2}\frac{2x^{2}+7x - 22}{x^{2}-4}=$ (type an integer or a simplified fraction.) b. the limit does not exist

Explanation:

Step1: Factor the polynomials

$2x^{2}+7x - 22=(2x + 11)(x - 2)$ and $x^{2}-4=(x + 2)(x - 2)$

Step2: Simplify the function

$\lim_{x
ightarrow2}\frac{2x^{2}+7x - 22}{x^{2}-4}=\lim_{x
ightarrow2}\frac{(2x + 11)(x - 2)}{(x + 2)(x - 2)}=\lim_{x
ightarrow2}\frac{2x+11}{x + 2}$

Step3: Substitute x = 2

$\frac{2\times2+11}{2 + 2}=\frac{4 + 11}{4}=\frac{15}{4}$

Answer:

A. $\frac{15}{4}$