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Continuity and Differentiability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsContinuity and Differentiability1 Mark
MCQ
If $f(x)=\left\{\begin{array}{l}x, \text { if } x \leq 1 \\ 7, \text { if } x > 1\end{array}\right.,$ then
  • A
    $\lim _{x \rightarrow 1^{-}} f(x)=7$
  • B
    $f$ is continuous at $x=1$
  • C
    $\lim _{x \rightarrow 1^{+}} f(x)=1$
  • ✓
    $f$ is discontinuous at $x=1$
✓

Answer

Correct option: D.
$f$ is discontinuous at $x=1$
$f(1)=1$
$\lim _{x \rightarrow 1^{-}} f(x)=\lim _{x \rightarrow 1} x=1, \lim _{x \rightarrow 1^{+}} f(x)$
$=\lim _{x \rightarrow 1} 7=7$
Since, $f(1) \neq \lim _{x \rightarrow 1^{+}} f(x)$
$\therefore f$ is discontinuous at $x=1$

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