Question

Evaluate: $\underset{x\to 2}{lim}\{\frac{1}{x-2}-\frac{4}{x^2-4}\}$

• A. $0$
• B. $4$
• C. $\frac{1}{4}$
• D. $-\frac{1}{4}$

Answer 1

The correct option is C $\frac{1}{4}$

$\underset{x\to 2}{lim}\{\frac{1}{x-2}-\frac{4}{x^2-4}\}$

$=\underset{x\to 2}{lim}\{\frac{1}{x-2}-\frac{4}{(x+2)(x-2))}\}$

$=\underset{x\to 2}{lim}\frac{x+2-4}{(x+2)(x-2)}$

$=\underset{x\to 2}{lim}\frac{(x-2)}{(x+2)(x-2)}$

$=\underset{x\to 2}{lim}\frac{1}{x+2}$

$=\frac{1}{4}$