Functions Question 330
Question: If f is strictly increasing function, then $ \underset{x\to 0}{\mathop{\lim }},\frac{f(x^{2})-f(x)}{f(x)-f(0)} $ is equal to
[IIT Screening 2004]
Options:
A) 0
B) 1
C) -1
D) 2
Show Answer
Answer:
Correct Answer: C
Solution:
$ \underset{x\to 0}{\mathop{\lim }},\frac{f(x^{2})-f(x)}{f(x)-f(0)} $ , $ ( \frac{0}{0}form ) $
$ =\underset{x\to 0}{\mathop{\lim }},\frac{2xf’(x^{2})-f’(x)}{f’(x)} $ , (using L’ Hospital’s rule)
$ =-1+\underset{x\to 0}{\mathop{\lim }},\frac{2xf’(x^{2})}{f’(x)}=-1,f’(0)\ne 0,, $
as f is strictly increasing.
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