Question

If $f\left(a\right)=2$, $f^{{}^{\prime }}\left(a\right)=1$, $g\left(a\right)=-1$, $g^{{}^{\prime }}\left(a\right)=2$ then $\underset{x\to a}{lim}\frac{g\left(x\right)f\left(a\right)-g\left(a\right)f\left(x\right)}{x-a}$ is

• A. $-5$
• B. $\frac{1}{5}$
• C. $5$
• D. none of these

Answer 1

Answer: (C)

$5$

By L'Hospital's Rule,
$=\underset{x\to a}{lim}\frac{g^{\prime }\left(x\right)f\left(a\right)-f^{\prime }\left(x\right)g\left(a\right)}{1}$
$=\frac{4+1}{1}=5$