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Example 14 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at Dec. 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 14 Show that every polynomial function is continuousLet π(π)=π_π+π_π π+π_π π^π+ β¦ +π_π π^π πβπ be a polynomial function Since Polynomial function is valid for every real number We prove continuity of Polynomial Function at any point c Let c be any real number f(x) 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_0+π_1 π₯+ β¦ +π_π π₯^π ) Putting x = c = π_0+π_1 π+ β¦ +π_π π^π R.H.S π(π) = π_0+π_1 π+ β¦ +π_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 all π βπ i.e. Every polynomial function is continuous.
