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. $3$
• C. $-3$
• D. $5$

Answer 1

Answer: (C)

$-3$

$\underset{x\to a}{lim}\frac{g\left(x\right)f\left(a\right)-g\left(a\right)f\left(x\right)}{x-a}$
Applying L-Hospital's rule,
$=\underset{x\to a}{lim}\frac{f\left(a\right)g^{{}^{\prime }}\left(x\right)-g\left(a\right)f^{{}^{\prime }}\left(x\right)}{1}$
$=-4-(-1)=-3$