Question

Estimate the limit.

Answer 1

Answer:

The correct answer option is A. 0.25.

Step-by-step explanation:

We are given the following expression and we are to find its limit:

$lim_\left \{ {{ x = 2 }$ $\frac { x - 2 } { x ^ 2 - 4 }$.

First of all, we will simplify the expression by factorizing the term in the denominator:

$\frac { x - 2 } { x ^ 2 - 4 } = \frac { x - 2 } { ( x - 2 ) ( x + 2 ) }$

Cancelling the common terms to get:

$\frac{1}{x+2}$

Substituting the given value for x to get:

$\frac{1}{2+2}$ = 0.25

Answer 2

Answer:

a. 0.25

Step-by-step explanation:

The given expression is

$\lim_{x \to 2} \frac{x-2}{x^2-4}$

Factor the denominator using difference of two squares.

$\lim_{x \to 2} \frac{x-2}{(x-2)(x+2)}$

Cancel out common factors;

$\lim_{x \to 2} \frac{1}{(x+2)}$

We plug in 2 to get

$\lim_{x \to 2} \frac{1}{(x+2)}=\frac{1}{2+2}$

$\lim_{x \to 2} \frac{1}{(x+2)}=\frac{1}{4}=0.25$