Question

If $f\left(2\right)=g\left(2\right)$ and $f^{\prime }\left(2\right)=a,g^{\prime }\left(2\right)=2a$

then $\underset{x\to 2}{lim}\frac{f\left(x\right)-g\left(x\right)}{x-2}$ is equal to ?

• A. $1$
• B. $a$
• C. $-a$
• D. none of these

Answer 1

Answer: (C)

$-a$

${lim}_{x\to 2}\frac{f\left(x\right)-g\left(x\right)}{x-2}=\frac{f\left(2\right)-g\left(2\right)}{2-2}\frac{0}{0}$

$={lim}_{x\to 2}\frac{f^{\prime }\left(x\right)-g^{\prime }\left(x\right)}{1}=f^{\prime }\left(2\right)-g^{\prime }\left(2\right)$

$=a-2a=-a$