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Home  >>  CBSE XI  >>  Math  >>  Limits and Derivatives
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Find $ \lim\limits_{x \to 0} f(x) $ and $ \lim\limits_{x \to 1} f(x) $ where $f(x)=\left\{\begin{array}{1 1}2x+3, &x \leq 0\\ 3(x+1),& x > o\end{array}\right.$

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The given function is
$f(x)=\left\{\begin{array}{1 1}(2x+3), &x \leq 0\\ 3(x+1),& x > o\end{array}\right.$
$ \lim\limits_{x \to 0^-} f(x) = \lim\limits_{x \to 0} [2x+3]= 2(0)+3 = 3$
$ \lim\limits_{x \to 0^+} f(x) = \lim\limits_{x \to 0}3(x+1) = 3( 0+1) =3$
$ \therefore \lim\limits_{x \to 0^-} f(x) = \lim\limits_{x \to 0^+} f(x) = \lim\limits_{x \to 0} f(x) = 3$
$ \lim\limits_{x \to 1^-} f(x) = \lim\limits_{x \to 1}3(x+1) = 3(1+1) = 6$
$ \lim\limits_{x \to 1^+} f(x) = \lim\limits_{x \to 1}3(x+1) = 3(1+1) = 6$
$ \therefore \lim\limits_{x \to 1^-} f(x) = \lim\limits_{x \to 1^+} f(x) = \lim\limits_{x \to 1} f(x) = 6$
answered Apr 5, 2014 by thanvigandhi_1
 

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