Last updated at March 12, 2021 by Teachoo

Transcript

Example 16 Prove that every rational function is continuous.Every Rational function ๐(๐ฅ) is of the form ๐(๐)= ๐(๐)/๐(๐) where ๐(๐ฅ) โ 0 & ๐, ๐ are polynomial functions Since ๐(๐ฅ) & ๐(๐ฅ) 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 are continuous , then ๐/๐ is continuous. Thus, Rational Function ๐(๐ฅ)= ๐(๐ฅ)/๐(๐ฅ) is continuous for all real numbers except at points where ๐(๐) = 0

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Chapter 5 Class 12 Continuity and Differentiability

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About the Author

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.