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Ex 5.1, 22 (iii) - Chapter 5 Class 12 Continuity and Differentiability - Part 2

  1. Chapter 5 Class 12 Continuity and Differentiability (Term 1)
  2. Serial order wise


Ex 5.1, 22 (iii) Discuss the continuity of the cosine, cosecant, secant and cotangent functions. Let ๐’‡(๐’™)="sec x" ๐‘“(๐‘ฅ) = 1/c๐‘œ๐‘ โก๐‘ฅ Let ๐’‘(๐’™)=1 & ๐’’(๐’™)=๐‘๐‘œ๐‘ โก๐‘ฅ Since, p(x) is a constant, โˆด ๐‘(๐‘ฅ) is continuous We know that cosโก๐‘ฅ is continuous for all real number โˆด ๐‘ž(๐‘ฅ) is continuous By Algebra of continuous function If ๐‘, ๐‘ž are continuous , then ๐’‘/๐’’ is continuous. Thus, ๐‘“(๐‘ฅ) = 1/cosโก๐‘ฅ is continuous for all real numbers except points where cosโก๐‘ฅ = 0 i.e. ๐’™=(๐Ÿ๐’+๐Ÿ) ๐…/๐Ÿ, ๐‘›โˆˆ๐’ So, ๐’”๐’†๐’„ ๐’™ is continuous at all real numbers except where ๐’™=(๐Ÿ๐’+๐Ÿ) ๐…/๐Ÿ, ๐’โˆˆ๐’

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.