Differentiation Question 292
Question: If $ f(x) $ has a derivative at $ x=a, $ then $ \underset{x\to a}{\mathop{\lim }}\frac{xf(a)-af(x)}{x-a} $ is equal to
[AMU 2000]
Options:
A) $ f(a)-af’(a) $
B) $ af(a)-f’(a) $
C) $ f(a)+f’(a) $
D) $ af(a)+f’(a) $
Show Answer
Answer:
Correct Answer: A
Solution:
$ \underset{x\to a}{\mathop{\lim }}\frac{xf(a)-af(x)}{x-a} $
$ =\underset{x\to a}{\mathop{\lim }}\frac{xf(a)-af(a)-af(x)+af(a)}{x-a} $
= $ \underset{x\to a}{\mathop{\lim }}\frac{f(a)(x-a)-a[f(x)-f(a)]}{x-a} $ = $ f(a)-a{f}’(a) $ .
BETA
