Solved on Nov 03, 2023

Find the limit as $x$ approaches -1 for $\frac{x^{2}-1}{2 x^{2}+3 x+1}$ . Enter the result or "inf"/"-inf".

STEP 1

Assumptions1. We are asked to evaluate the limit of the function $\frac{x^{}-1}{ x^{}+3 x+1}$ as x approaches -1. . We assume that the function is defined at all real numbers except possibly at x = -1.

STEP 2

First, let's try to substitute x = -1 directly into the function and see if it is defined at that point.
$f(-1) = \frac{(-1)^{2}-1}{2 (-1)^{2}+ (-1)+1}$

STEP 3

Calculate the value of the function at x = -1.
$f(-1) = \frac{1-1}{2+3+1}$

STEP 4

implify the expression.
$f(-1) = \frac{0}{6}$

STEP 5

Calculate the value of the function at x = -1.
$f(-1) =0$ Since the function is defined at x = -1 and its value is0, the limit of the function as x approaches -1 is0.

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