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trasher [3.6K]
3 years ago
7

Estimate the limit.

Mathematics
2 answers:
adell [148]3 years ago
6 0

<u>Answer:</u>

The correct answer option is A. 0.25.

<u>Step-by-step explanation:</u>

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

Bezzdna [24]3 years ago
3 0

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

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