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Example 16 - Prove that every rational function is continuous

Example 16 - Chapter 5 Class 12 Continuity and Differentiability - Part 2


Example 16 Prove that every rational function is continuous.Every Rational function 𝑓(π‘₯) is of the form 𝒇(𝒙)= 𝒑(𝒙)/𝒒(𝒙) where π‘ž(π‘₯) β‰  0 & 𝑝, π‘ž are polynomial functions Since 𝑝(π‘₯) & π‘ž(π‘₯) are polynomials, and we know that every polynomial function is continuous. Therefore, 𝒑(𝒙) & 𝒒(𝒙) both continuous By Algebra of continuous function If 𝑝, π‘ž are continuous , then 𝒑/𝒒 is continuous. Thus, Rational Function 𝑓(π‘₯)= 𝑝(π‘₯)/π‘ž(π‘₯) is continuous for all real numbers except at points where 𝒒(𝒙) = 0

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.