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CONTINUITY AND DIFFERENTIABILITY — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsCONTINUITY AND DIFFERENTIABILITY1 Mark
Question
Choose the correct answers from the given four options:
The function $\text{f(x)}=\cot\text{x}$ is discontinuous on the set
  1. $\big\{\text{x}=\text{n}\pi:\text{n}\in\text{Z}\big\}$
  2. $\big\{\text{x}=2\text{n}\pi:\text{n}\in\text{Z}\big\}$
  3. $\Big\{\text{x}=(2\text{n}+1)\frac{\pi}{2};\text{n}\in\text{Z}\Big\}$
  4. $\Big\{\text{x}=\frac{\text{n}\pi}{2};\text{n}\in\text{Z}\Big\}$
✓

Answer

  1. $\big\{\text{x}=\text{n}\pi:\text{n}\in\text{Z}\big\}$

Solution:

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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