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  • The function f(x) = cot x is discontinuous on the set A.{X=n\pi:n belongs Z}

The functionf(x) = \cot x is discontinuous on the set
 \\A. \{x=n \pi: n \in Z\} \\B. \{x=2 n \pi: n \in Z\} \\C. \left\{x=(2 n+1) \frac{\pi}{2} ; n \in \mathbf{Z}\right\} \\D. \left\{\mathrm{x}=\frac{\mathrm{n} \pi}{2} ; \mathrm{n} \in \mathrm{Z}\right\}

Answers (1)

We have, f(x) = \cot x = \frac{\cos x}{\sin x}

Now, f(x) is discontinuous where sinx=0

We know that sinx=0 at x = nπ, n ∈ Z

⇒ f(x) = cotx is discontinuous on the set {x = nπ : n ∈ Z}

 

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infoexpert22

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