Example 16 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Example 16 Prove that every rational function is continuous.Every Rational function 𝑓(𝑥) is of the form 𝒇(𝒙)= 𝒑(𝒙)/𝒒(𝒙) where 𝑞(𝑥) ≠ 0 & 𝑝, 𝑞 are polynomial functions Since 𝑝(𝑥) & 𝑞(𝑥) 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, 𝑞 are continuous , then 𝒑/𝒒 is continuous. Thus, Rational Function 𝑓(𝑥)= 𝑝(𝑥)/𝑞(𝑥) is continuous for all real numbers except at points where 𝒒(𝒙) = 0
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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