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Home  >>  CBSE XI  >>  Math  >>  Limits and Derivatives
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Find $ \lim\limits_{x \to 5}f(x)$ where, $ f(x) = |x|-5$

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The given function is $ f(x) = |x|-5$
$ \lim\limits_{x \to 5^-} f(x) = \lim\limits_{x \to 5^-} [|x| -5]$
$\lim\limits_{x \to 5} (x-5)$ $ \quad \quad [where\: x > 0, |x| = x]$
$ = 5-5$
$ = 0$
$ \lim\limits_{x \to 5^+} f(x) = \lim\limits_{x \to 5^+} [|x| -5]$
$\lim\limits_{x \to 5} (x-5)$ $ \quad \quad [where\: x > 0, |x| = x]$
$ = 5-5$
$ = 0$
$ \therefore \lim\limits_{x \to 5^-} f(x) = \lim\limits_{x \to 5^+} f(x) =0$
Hence, $ \lim\limits_{x \to 5} f(x) =0$
answered Apr 5, 2014 by thanvigandhi_1
 

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