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Ex 5.8, 2 - Chapter 5 Class 12 Continuity and Differentiability (Term 1)
Last updated at Aug. 19, 2021 by Teachoo
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
Ex 5.8, 2 Examine if Rolle’s theorem is applicable to the functions. Can you say some thing about the converse of Rolle’s theorem from this function? (𝑖) 𝑓 (𝑥) = [𝑥] 𝑓𝑜𝑟 𝑥 ∈ [5, 9]Greatest Integer less than equal to 𝑥 𝑓 (𝑥) =[𝑥] is not continuous & differentiable ⇒ Condition of Rolle’s Theorem is not satisfied. Therefore, Rolle’s Theorem is not applicable .
