use properties of limits to find the indicated limit. it may be necessary to rewrite the expression before…

use properties of limits to find the indicated limit. it may be necessary to rewrite the expression before limit properties can be applied. lim x→5 x² + 2x - 35 / x² - 25 select the correct choice below and fill in any answer boxes in your choice. a. lim x→5 x² + 2x - 35 / x² - 25 = (type an integer or a simplified fraction.) b. the limit does not exist.

use properties of limits to find the indicated limit. it may be necessary to rewrite the expression before limit properties can be applied. lim x→5 x² + 2x - 35 / x² - 25 select the correct choice below and fill in any answer boxes in your choice. a. lim x→5 x² + 2x - 35 / x² - 25 = (type an integer or a simplified fraction.) b. the limit does not exist.

Answer

Explanation:

Step1: Factor the numerator and denominator

The numerator $x^{2}+2x - 35=(x + 7)(x - 5)$ and the denominator $x^{2}-25=(x + 5)(x - 5)$. So the limit becomes $\lim_{x\rightarrow5}\frac{(x + 7)(x - 5)}{(x + 5)(x - 5)}$.

Step2: Cancel out the common factor

Cancel out the common factor $(x - 5)$ (since $x\neq5$ when taking the limit), we get $\lim_{x\rightarrow5}\frac{x + 7}{x + 5}$.

Step3: Substitute $x = 5$

Substitute $x = 5$ into $\frac{x + 7}{x + 5}$, we have $\frac{5+7}{5 + 5}=\frac{12}{10}=\frac{6}{5}$.

Answer:

A. $\lim_{x\rightarrow5}\frac{x^{2}+2x - 35}{x^{2}-25}=\frac{6}{5}$