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Question
The function f(x) = cot x is discontinuous on the set ______.
Options
{x = nπ : n ∈ Z}
{x = 2nπ : n ∈ Z}
`{x = (2"n" + 1)pi/2 ; "n" ∈ "Z"}`
`{x = ("n"pi)/2 ; "n" ∈ "Z"}`
Solution
The function f(x) = cot x is discontinuous on the set {x = nπ : n ∈ Z}.
Explanation:
Given that: f(x) = cot x
⇒ f(x) = `cosx/sinx`
We know that sin x = 0 if f(x) is discontinuous.
∴ If sin x = 0
∴ x = nπ, n ∈ nπ.
So, the given function f(x) is discontinuous on the set {x = nπ : n ∈ Z}.
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