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Example 1 - 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 1 Check the continuity of the function f given by f (x) = 2x + 3 at x = 1. π(π₯) is continuous at π₯=1 if limβ¬(xβ1) π(π₯) = π(1) (π₯π’π¦)β¬(π±βπ) π(π) "= " limβ¬(xβ1) " "(2π₯+3) = 2 Γ 1 + 3 = 2 + 3 = 5 (π₯π’π¦)β¬(π±βπ) π(π) "= " limβ¬(xβ1) " "(2π₯+3) = 2 Γ 1 + 3 = 2 + 3 = 5 π(π) = 2 Γ 1 + 3 = 2 + 3 = 5 π(π) = 2 Γ 1 + 3 = 2 + 3 = 5 Since, L.H.S = R.H.S β΄ Function is continuous.
