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Ex 5.1 ,2 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at April 16, 2024 by Teachoo
Checking continuity at a given 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
Ex 5.1, 2 Examine the continuity of the function f (x) = 2x2 β 1 at x = 3. π(π₯) is continuous at x = 3 if limβ¬(xβ3) π(π₯) = π(3) Since, L.H.S = R.H.S Hence, f is continuous at π =3 (π₯π’π¦)β¬(π±βπ) π(π) "= " limβ¬(xβ3) " "(2π₯2β1) Putting π₯ = 3 = 2(3)2 β 1 = 2 Γ 9 β 1 = 17 π(π) = 2(3)2 β 1 = 2 Γ 9 β 1 = 18β1 = 17
