Question

What is Limit of StartFraction x minus 1 Over x squared minus 1 EndFraction as x approaches negative 1? –2 –1 0 DNE

ANSWER: D

Answer 1

Explanation:

Limit of (x - 1))/(x^2 - 1)

x---> -1

As x approaches -1 from negative side ( x < -1) the limit is -infinity.

As x approaches -1 from positive side ( x > -1) the limit is +infinity

Answer 2

The limits of the expression
`\lim_(x \to -1) (x-1)/(x^2 - 1)` as x approaches negative 1 is (d) DNE

How to determine the limits of the expression

From the question, we have the following parameters that can be used in our computation:

`\lim_(x \to -1) (x-1)/(x^2 - 1)`

Apply the difference of two squares to simplify the denominator

So, we have

`\lim_(x \to -1) (x-1)/(x^2 - 1)=\lim_(x \to -1) (x-1)/((x - 1)(x + 1))`

Cancel out the common factors

This gives

`\lim_(x \to -1) (x-1)/(x^2 - 1) = \lim_(x \to -1) (1)/(x + 1)`

Substitute -1 for x

`\lim_(x \to -1) (x-1)/(x^2 - 1) = (1)/(-1 + 1)`

This gives

`\lim_(x \to -1) (x-1)/(x^2 - 1) =(1)/(0)`

Evaluate

`\lim_(x \to -1) (x-1)/(x^2 - 1) = \text{DNE}`

Hence. the limits of the expression as x approaches negative 1 is (d) DNE