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Example 16 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at August 13, 2026 by Teachoo
Checking continuity at any point
Chapter 5 Class 12 Continuity and Differentiability
Concept wise
- Checking continuity at a given point
-
Checking continuity at any point
- Checking continuity using LHL and RHL
- Algebra of continous functions
- Continuity of composite functions
- Checking if funciton is differentiable
- Finding derivative of a function by chain rule
- Finding derivative of Implicit functions
- Finding derivative of Inverse trigonometric functions
- Finding derivative of Exponential & logarithm functions
- Logarithmic Differentiation - Type 1
- Logarithmic Differentiation - Type 2
- Derivatives in parametric form
- Finding second order derivatives - Normal form
- Finding second order derivatives- Implicit form
- Proofs
- Verify Rolles theorem
- Verify Mean Value Theorem
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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
