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for what value of k is the following function continuous at x=2? f(x)={2x+1 ;x<2 { k;x=2 { 3x-1;x>2

Posted by Ajit Shrivastav 11 A 2 years, 3 months ago

CBSE > Class 12 > Mathematics

1 answers

Preeti Dabral 2 years, 3 months ago

$\mathop {\lim }\limits_{x \to {2^ - }} f(x) = \mathop {\lim }\limits_{x \to {2^ - }} 2x + 1$
$\mathop {\lim }\limits_{h \to 0} \left[ {2\left( {2 - h} \right) + 1} \right]$ = 5
$= \mathop {\lim }\limits_{x \to {2^ + }} f(x) = \mathop {\lim }\limits_{x \to {2^ + }} \left( {3x -1} \right)$
$= \mathop {\lim }\limits_{h \to 0} 3\left( {2 + h} \right) - 1$ = 5
In given that question f(x) is continuous at x=2,therefore
$\mathop {\lim }\limits_{x \to {2^ - }} f(x) = f(2) = \mathop {\lim }\limits_{x \to {2^ + }} f(x)$
5 = k
$\Rightarrow k = 5$

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