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The function f (x) = cot x is discontinuous on the set

(A) {x=nΟ€:n∈ Z} Β  Β Β  Β  Β Β Β Β Β Β Β Β 

(B) {x=2nΟ€:n∈ Z} Β 

(C) {x= (2n+1)Β  Ο€/2 Β  ; n ∈z} Β  Β Β Β Β Β Β Β Β  Β  Β Β Β Β Β Β Β Β 

(D) {x= n Ο€/2 Β  ; n ∈z}

This question is similar to Example 18 - Chapter 5 Class 12 - Continuity and Differentiability

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Question 16 The function f (x) = cot x is discontinuous on the set (A) {π‘₯=π‘›πœ‹:π‘›βˆˆπ’} (B) {π‘₯=2π‘›πœ‹:π‘›βˆˆπ’} (C) {π‘₯=(πŸπ’+𝟏) 𝝅/𝟐 ;π‘›βˆˆπ’›} (D) {π‘₯=𝒏𝝅/𝟐 ;π‘›βˆˆπ’›} Let 𝑓(π‘₯) = cπ‘œπ‘‘β‘π‘₯ 𝒇(𝒙) = 𝒄𝒐𝒔⁑𝒙/π’”π’Šπ’β‘π’™ Here, 𝑓(π‘₯) is defined for all real number except π’”π’Šπ’β‘π’™ = 0 i.e. for all x except x = 𝒏𝝅 Thus, cot⁑π‘₯ is discontinuous on the set {𝒙=𝒏𝝅:π’βˆˆπ’} So, the correct answer is (A)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.