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Continuity and Differentiability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsContinuity and Differentiability1 Mark
MCQ
Choose the correct answers from the given four options : The function $\text{f(x)}=\cot\text{x}$ is discontinuous on the set
  • ✓
    $\big\{\text{x}=\text{n}\pi:\text{n}\in\text{Z}\big\}$
  • B
    $\big\{\text{x}=2\text{n}\pi:\text{n}\in\text{Z}\big\}$
  • C
    $\Big\{\text{x}=(2\text{n}+1)\frac{\pi}{2};\text{n}\in\text{Z}\Big\}$
  • D
    $\Big\{\text{x}=\frac{\text{n}\pi}{2};\text{n}\in\text{Z}\Big\}$
✓

Answer

Correct option: A.
$\big\{\text{x}=\text{n}\pi:\text{n}\in\text{Z}\big\}$
Consider, $\text{f(x)}=\cos\text{x}=\frac{\cos\text{x}}{\sin\text{x}}$
We know that, $\big[\sin\text{x}=0\text{ at }\text{x}=\text{n}\pi,\text{n}\in\text{Z}\big]$
Hence, $\text{f(x)}=\cot\text{x}$ is discontinuous on the set $\big\{\text{x}=\text{n}\pi:\text{n}\in\text{Z}\big\}.$

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