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STD 12 - 5. continuity and differentiation — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 5. continuity and differentiation1 Mark
MCQ
The function $'f'$ is defined by $f(x) = \left\{ {\begin{array}{*{20}{c}}{ 2x - 1,}&{if \,\,\, x > 2}\\{k,}&{ if \,\,\,x=2}\\{{x^2} - 1,}&{if \,\,\, x < 2 }\end{array}} \right.$ is continuous, then the value of $k$ is equal to
  • A
    $2$
  • ✓
    $3$
  • C
    $4$
  • D
    $-3$
✓

Answer

Correct option: B.
$3$
b
(b) We have $f(x) = 2x - 1,$ if $x > 2,$ $f(x) = k,$

If $x = 2$ and ${x^2} - 1,$ if $x < 2$, function is continuous.

$\therefore $ $\mathop {\lim }\limits_{x \to 2} f(x) = f(2)$==> $\mathop {\lim }\limits_{x \to 2} (2x - 1) = k \Rightarrow k = 3$.

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