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Example 2 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at December 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
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Transcript
Example 2 Examine whether the function f given by π (π₯) = π₯2 is continuous at π₯ = 0 π(π₯) is continuous at π₯ = 0 if limβ¬(xβ0) π(π₯) = π(0) L.H.S (π₯π’π¦)β¬(π±βπ) π(π) "= " limβ¬(xβ0) " " π₯2 Putting π₯ = 0 = (0)2 = 0 R.H.S π(π) = (0)2 = 0 Since LHS = RHS Hence, f(x) is continuous at x = 0
