Ex 5.1, 22 (iii) - Chapter 5 Class 12 Continuity and Differentiability
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Ex 5.1, 22 (iii) Discuss the continuity of the cosine, cosecant, secant and cotangent functions. Let 𝒇(𝒙)="sec x" 𝑓(𝑥) = 1/c𝑜𝑠𝑥 Let 𝒑(𝒙)=1 & 𝒒(𝒙)=𝑐𝑜𝑠𝑥 Since, p(x) is a constant, ∴ 𝑝(𝑥) is continuous We know that cos𝑥 is continuous for all real number ∴ 𝑞(𝑥) is continuous By Algebra of continuous function If 𝑝, 𝑞 are continuous , then 𝒑/𝒒 is continuous. Thus, 𝑓(𝑥) = 1/cos𝑥 is continuous for all real numbers except points where cos𝑥 = 0 i.e. 𝒙=(𝟐𝒏+𝟏) 𝝅/𝟐, 𝑛∈𝒁 So, 𝒔𝒆𝒄 𝒙 is continuous at all real numbers except where 𝒙=(𝟐𝒏+𝟏) 𝝅/𝟐, 𝒏∈𝒁
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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo