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# If $f(x)=3x^{10}-7x^8+5x^6-21x^3+3x^2-7$ then value of $\lim\limits_{\alpha \to 0}\large\frac{f(1-\alpha)-f(1)}{\alpha^3+3\alpha}$ is

$(a)\;\large\frac{53}{3}$$\qquad(b)\;\large\frac{22}{3}$$\qquad(c)\;13\qquad(d)\;None\;of\;these$

Can you answer this question?

$\lim\limits_{\alpha\to 0}\large\frac{f(1-\alpha)-f(1)}{\alpha^3+3\alpha}$
$\Rightarrow \lim\limits_{\alpha\to 0}\large\frac{f(1-\alpha)-f(1)}{-\alpha}.\frac{-1}{\alpha^2+3}$
$\Rightarrow f'(1).\big(\large\frac{-1}{3}\big)$
$\Rightarrow \large\frac{53}{3}$
Hence (a) is the correct answer.
answered Jan 2, 2014
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