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If function $f(x)$ is differentiable at $x=a$ then $\lim\limits_{x\to a}\large\frac{x^2f(a)-a^2f(x)}{x-a}$ is

$\begin{array}{1 1}(a)\;-a^2f'(a)&(b)\;af(a)-a^2f'(a)\\(c)\;2af(a)-a^2f'(a)&(d)\;2af(a)+a^2f'(a)\end{array}$

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$\lim\limits_{x\to a}\large\frac{x^2f(a)-a^2f(a)}{x-a}=$$\lim\limits_{x\to a}\large\frac{2xf(a)-a^2f'(x)}{1}$
$\Rightarrow 2af(a)-a^2f'(a)$
Hence (c) is the correct answer.
answered Dec 23, 2013 by sreemathi.v

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