Ex 5.1

Ex 5.1 ,1

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Ex 5.1, 3 (a)

Ex 5.1, 3 (b)

Ex 5.1, 3 (c) Important

Ex 5.1, 3 (d) Important

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Ex 5.1, 20

Ex 5.1, 21

Ex 5.1, 22 (i) Important

Ex 5.1, 22 (ii)

Ex 5.1, 22 (iii) You are here

Ex 5.1, 22 (iv) Important

Ex 5.1, 23

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Last updated at April 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