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5. continuity and differentiation — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
MCQ
The function $f(x)\, = \left\{ \begin{array}{l}x + 2\,\,\,\,,\,\,\,1 \le x \le 2\\4\,\,\,\,\,\,\,\,\,\,\,,\,\,\,x = 2\\3x - 2\,\,,\,\,\,x > 2\end{array} \right.$ is continuous at
  • A
    $x = 2$ only
  • B
    $x \le 2$
  • ✓
    $x \ge 2$
  • D
    None of these
✓

Answer

Correct option: C.
$x \ge 2$
c
(c) Clearly the function is defined only in the interval $[1,\,\infty )$

hence option $(b)$ cannot even apply.

For $x > 2,\,y = 3x - 2$ which is a straight line, hence continuous. 

Further $y = 4$ at $x = 2$.

Hence, the function is continuous at $x = 2$ also (but not at $x = 2$ only).

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