Question

Evaluate $\underset{x\to 2}{lim}\frac{f\left(x\right)-f\left(2\right)}{x-2}$ where f(x)=$x^2-4$

• A. -1
• B. 2
• C. 0
• D. 4

Answer 1

The correct option is D 4

Given, $f\left(x\right)=x^2-4$
So, $f\left(2\right)=2^2-4=0$
Now, $\underset{x\to 2}{lim}\frac{f\left(x\right)-f\left(2\right)}{x-2}=\underset{x\to 2}{lim}\frac{x^2-4-0}{x-2}=\underset{x\to 2}{lim}\frac{(x+2)(x-2)}{x-2}=\underset{x\to 2}{lim}(x+2)$
Substituting $x=2$, we get $2+2=4$
Thus, $\underset{x\to 2}{lim}\frac{f\left(x\right)-f\left(2\right)}{x-2}=4$