Continuity And Differentiability

Question

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For what value of k is the following function continuous at x = 2?
$f (x) = \begin{matrix} 2 x + 1; x < 2 \\ k; x = 2 \\ 3 x - 1; x > 1 \end{matrix}$

Solution

The given function f(x) will be continuous at x = 2, if

$\lim_{x \to 2^{-}} f (x) = \lim_{x \to 2^{+}} f (x) = f (2) \lim_{x \to 2^{-}} f (x) = \lim_{x \to 2^{-}} 2 x + 1 = 2 x 2 + 1 = 5 \lim_{x \to 2^{+}} f (x) = \lim_{x \to 2^{+}} 3 x - 1 = 3 x 2 - 1 = 5 ∴ f (2) = k \Rightarrow k = 5$

Thus, for k = 5, the given function is continuous at x = 2.

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Continuity And Differentiability

For what value of k is the following function continuous at x = 2?
$f (x) = \begin{matrix} 2 x + 1; x < 2 \\ k; x = 2 \\ 3 x - 1; x > 1 \end{matrix}$

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For Daily Free Study Material Join wiredfaculty

Continuity And Differentiability

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>1

Some More Questions From Continuity and Differentiability Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

For what value of k is the following function continuous at x = 2?
$f (x) = \begin{matrix} 2 x + 1; x < 2 \\ k; x = 2 \\ 3 x - 1; x > 1 \end{matrix}$