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→1 x² + 3x - 4 / x² - 1. select the correct choice below and, if necessary, fill in the answer box to complete your choice. o a. lim x→1 x² + 3x - 4 / x² - 1 = (type an integer or a simplified fraction.) o b. the limit does not exist and is neither ∞ nor -∞. use properties of limits to find the indicated limit. it may be necessary to rewrite the expression before limit properties can be applied.

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→1 x² + 3x - 4 / x² - 1. select the correct choice below and, if necessary, fill in the answer box to complete your choice. o a. lim x→1 x² + 3x - 4 / x² - 1 = (type an integer or a simplified fraction.) o b. the limit does not exist and is neither ∞ nor -∞. use properties of limits to find the indicated limit. it may be necessary to rewrite the expression before limit properties can be applied.

Answer

Explanation:

Step1: Factor the numerator and denominator

The numerator $x^{2}+3x - 4=(x + 4)(x - 1)$ and the denominator $x^{2}-1=(x + 1)(x - 1)$. So the function becomes $\lim_{x\rightarrow1}\frac{(x + 4)(x - 1)}{(x + 1)(x - 1)}$.

Step2: Simplify the function

Cancel out the common factor $(x - 1)$ (since $x\neq1$ when taking the limit), we get $\lim_{x\rightarrow1}\frac{x + 4}{x + 1}$.

Step3: Apply the limit property

Substitute $x = 1$ into $\frac{x+4}{x + 1}$, we have $\frac{1+4}{1+1}=\frac{5}{2}$.

Answer:

A. $\lim_{x\rightarrow1}\frac{x^{2}+3x - 4}{x^{2}-1}=\frac{5}{2}$