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$\lim\limits_{x\to 1}\large\frac{x^3+x^2-2}{\sin(x-1)}$ is

$(a)\;2\qquad(b)\;5\qquad(c)\;3\qquad(d)\;None\;of\;these$

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$\lim\limits_{x\to 1}\large\frac{x^3+x^2-2}{\sin(x-1)}=$$\lim\limits_{x\to 1}\large\frac{(x-1)(x^2+2x+2)}{\sin(x-1)}$
$\Rightarrow \lim\limits_{x\to 1}(x^2+2x+2)$
$\Rightarrow 1(1+2+2)$
$\Rightarrow 5$
Hence (b) is the correct answer.
answered Dec 23, 2013 by sreemathi.v
 
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