Question

*Fill in the blank: The function f(x) = cot x is discontinues on the set _________.*

1️⃣ {x = 2nπ, n ∈ Z}
2️⃣ {x = nπ, n ∈ Z}
3️⃣ {x = -nπ/2, n ∈ Z}
4️⃣ {x = (2n + 1)π/2, n ∈ Z}​

Answer 1

Answer:

Hey!!

I guess the answer is 2)

Answer 2

The function $f(x) = cot x$ is discontinues on the set (2) { ${x = n\pi$, $n$∈Z}

Step-by-step explanation:

Given:

The function $f(x) = cot x$

To find:

If the given function is discontinues on the set

Solution:

We know that $f(x) = cot x$  is continuous in $R-$ {$n\pi:n$∈$z$}

Since,

$f(x) = cot x$

$=\frac{cot x}{sin x}$ ,[Since $sin x=0$ at $n\pi$, $n$∈Z]

Hence, $f(x) = cot x$ is discontinues on the set (2) { ${x = n\pi$, $n$∈Z}