KCET · Maths · Continuity and Differentiability
The function \(f(x)=\cot x\) is discontinuous on every point of the set
- A \(\{x=2 n \pi ; n \in Z\}\)
- B \(\left\{x=(2 n+1) \frac{\pi}{2} ; n \in Z\right\}\)
- C \(\left\{x=\frac{n \pi}{2} ; n \in Z\right\}\)
- D \(\{x=n \pi ; n \in Z\}\)
Answer & Solution
Correct Answer
(D) \(\{x=n \pi ; n \in Z\}\)
Step-by-step Solution
Detailed explanation
Given, \(f(x)=\cot x\)
\(\Rightarrow \quad f(x)=\frac{\cos x}{\sin x}\)
We know that \(\sin x=0\), if \(f(x)\) is discontinuous
\(\therefore\) If \(\sin x=0\)
\(\therefore x=n \pi, n \in n \pi\)
So, the given function \(f(x)\) is discontinuous on the set \(\{x=n \pi, n \in Z\}\)
\(\Rightarrow \quad f(x)=\frac{\cos x}{\sin x}\)
We know that \(\sin x=0\), if \(f(x)\) is discontinuous
\(\therefore\) If \(\sin x=0\)
\(\therefore x=n \pi, n \in n \pi\)
So, the given function \(f(x)\) is discontinuous on the set \(\{x=n \pi, n \in Z\}\)
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