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Continuity and Differentiability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsContinuity and Differentiability1 Mark
MCQ
The function $\text{f(x)}=\tan\text{x}$ is discontinuous on the set :
  • A
    $\{\text{n}\pi:\text{n}\in\text{z}\}$
  • B
    $\{2\text{n}\pi:\text{n}\in\text{z}\}$
  • ✓
    $\{(2\text{n}+1)\frac{\pi}{2}:\text{n}\in\text{z}\}$
  • D
    $\Big\{\frac{\text{n}\pi}{2}:\text{n}\in\text{z}\Big\}$
✓

Answer

Correct option: C.
$\{(2\text{n}+1)\frac{\pi}{2}:\text{n}\in\text{z}\}$
When $\tan(2\text{n}+1)\frac{\pi}{2}=\tan\Big(\text{n}\pi+\frac{\pi}{2}\Big)=-\cot\text{n}\pi,$ it is not defined at the integral points.
$[\text{n}\in\text{z}]$
Hence, $f(x)$ is discontinuous on the set $\{(2\text{n}+1)\frac{\pi}{2}:\text{n}\in\text{z}\}$

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