Browse Questions

# If $f(a)=2$, $f'(a)=1$, $g(a)=-1$, $g'(a)=2$, then the value of $\lim\limits_{x\to a}\large\frac{g(x)f(a)-g(a)f(x)}{x-a}$ is

$(a)\;-5\qquad(b)\;1/5\qquad(c)\;5\qquad(d)\;None\;of\;these$

$\lim\limits_{x\to a}\large\frac{g(x)f(a)-g(a)f(x)}{x-a}$
$\Rightarrow \lim\limits_{h\to 0}\large\frac{g(a+h)f(a)-g(a)f(a+b)}{h}$
$\Rightarrow \lim\limits_{h\to 0}\large\frac{g(a+h)f(a)-g(a)f(a)+g(a)f(a)-g(a)f(a+b)}{h}$