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Value of $\lim_{x\to 2^-}\{x+(x-[x]^2)\}$ is

$(a)\;0\qquad(b)\;1\qquad(c)\;2\qquad(d)\;3$

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$\lim\limits_{x\to 2^-}\{x+(x-[x]^2)\}=\lim\limits_{h\to 0^+}\{2-h+(2h-[2-h]^2)\}$
$\Rightarrow \lim\limits_{h\to 0}\{2-h+(2-h+2-h-1)^2\}$
$\Rightarrow \{2-h+(3-2h)^2\}$
$\Rightarrow 3$
Hence (d) is the correct option.
answered Dec 24, 2013 by sreemathi.v
 

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