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If $(x)$ is differentiable and strictly increasing function then the value of $\lim\limits_{x\to 0}\large\frac{f(x^2)-f(x)}{f(x)-f(0)}$ is

$(a)\;1\qquad(b)\;0\qquad(c)\;-1\qquad(d)\;2$

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Let $L=\lim\limits_{x\to 0}\large\frac{f(x^2)-f(x)}{f(x)-f(0)}$
$f'(a) > 0$ $f$ being strictly increasing.
Using LH Rule we get
$L=\lim\limits_{x\to 0}\large\frac{f'(x^2).2x-f'(x)}{f'(x)}$$-1$
$\;\;\;=0-1$
$\;\;\;=-1$
Hence (c) is the correct answer.
answered Dec 20, 2013 by sreemathi.v
 

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