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Example 6 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at April 16, 2024 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
Transcript
Example 6 Prove that the identity function on real numbers given by f (x) = x is continuous at every real number.Given π(π₯)=π₯ To check continuity of π(π₯), We check itβs if it is continuous at any point x = c Let c be any real number f is continuous at π₯ =π if (π₯π’π¦)β¬(π±βπ) π(π)=π(π) L.H.S (π₯π’π¦)β¬(π±βπ) π(π) "= " limβ¬(xβπ) " " π₯ = π R.H.S π(π) = π Since, L.H.S = R.H.S β΄ Function is continuous at x = c Thus, we can write that f is continuous for x = c , where c βπ β΄ f is continuous for every real number.
