Ex 5.1, 28 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at Dec. 16, 2024 by Teachoo
Checking continuity using LHL and RHL
Example 12
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Chapter 5 Class 12 Continuity and Differentiability
Concept wise
- Checking continuity at a given point
- Checking continuity at any point
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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, 28 Find the values of k so that the function f is continuous at the indicated point π(π₯)={β(ππ₯+1 , ππ π₯β€π@cosβ‘γπ₯, γ ππ π₯>π)β€ at x = π Given that function is continuous at π₯ =π π is continuous at π₯ =π If L.H.L = R.H.L = π(π) i.e. limβ¬(xβπ^β ) π(π₯)=limβ¬(xβπ^+ ) " " π(π₯)= π(π) LHL at x β Ο (πππ)β¬(π₯βπ^β ) f(x) = (πππ)β¬(ββ0) f(Ο β h) = limβ¬(hβ0) k (Ο β h) + 1 = k(Ο β 0) + 1 = kΟ + 1 RHL at x β Ο (πππ)β¬(π₯βπ^+ ) f(x) = (πππ)β¬(ββ0) f(Ο + h) = limβ¬(hβ0) cos (Ο + h) = cos (Ο + 0) = cos (Ο) = β1 Since L.H.L = R.H.L ππ+1=β1 ππ=β2 π= (βπ)/π
