Example 16 - Chapter 5 Class 12 Continuity and Differentiability

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Example 16 - Prove that every rational function is continuous - Examples

part 2 - Example 16 - Examples - Serial order wise - Chapter 5 Class 12 Continuity and Differentiability

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

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