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


Example 16 Prove that every rational function is continuous.Every Rational function ๐‘“(๐‘ฅ) is of the form ๐’‡(๐’™)= ๐’‘(๐’™)/๐’’(๐’™) where ๐‘ž(๐‘ฅ) โ‰  0 & ๐‘, ๐‘ž are polynomial functions Since ๐‘(๐‘ฅ) & ๐‘ž(๐‘ฅ) are polynomials, and we know that every polynomial function is continuous. Therefore, ๐’‘(๐’™) & ๐’’(๐’™) both continuous By Algebra of continuous function If ๐‘, ๐‘ž are continuous , then ๐’‘/๐’’ is continuous. Thus, Rational Function ๐‘“(๐‘ฅ)= ๐‘(๐‘ฅ)/๐‘ž(๐‘ฅ) is continuous for all real numbers except at points where ๐’’(๐’™) = 0

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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.