Differentiation Question 309
Question: If $ f(x) $ is a differentiable function, then $ \underset{x\to a}{\mathop{\lim }}\frac{af(x)-xf(a)}{x-a} $ is
[UPSEAT 2002]
Options:
A) $ a{f}’(a)-f(a) $
B) $ af(a)-f’(a) $
C) $ a{f}’(a)+f(a) $
D) $ af(a)+f’(a) $
Show Answer
Answer:
Correct Answer: A
Solution:
$ \underset{x\to a}{\mathop{\lim }}\frac{af(x)-xf(a)}{x-a} $
Therefore $ \underset{x\to a}{\mathop{\lim }}\frac{af(x)-xf(a)+af(a)-af(a)}{x-a} $
Therefore $ \underset{x\to a}{\mathop{\lim }}\frac{a[f(x)-f(a)]-f(a)[x-a]}{x-a} $
Therefore $ \underset{x\to a}{\mathop{\lim }}\frac{a[f(x)-f(a)]}{x-a}-\underset{x\to a}{\mathop{\lim }}f(a) $
Therefore $ a{f}’(a)-f(a) $ .
BETA
