Example 3 - 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
Example 3 Discuss the continuity of the function f given by π(π₯) =|π₯| ππ‘ π₯ = 0. π(π₯) = |π₯| π(π₯)= {β(βπ₯, ππ π₯<0@π₯, ππ π₯ β₯0)β€ f is continuous at π₯ = 0 if L.H.L = R.H.L = π(0) i.e. (πππ)β¬(π₯β0^β ) π(π₯)=(πππ)β¬(π₯β0^+ ) π(π₯)=π(0) Finding LHL and RHL LHL at x β 0 limβ¬(xβ0^β ) f(x) = limβ¬(hβ0) f(0 β h) = limβ¬(hβ0) f(βh) = limβ¬(hβ0) \βh| = limβ¬(hβ0) h = 0 RHL at x β 0 limβ¬(xβ0^+ ) f(x) = limβ¬(hβ0) f(0 + h) = limβ¬(hβ0) f(h) = limβ¬(hβ0) \h| = limβ¬(hβ0) h = 0 And, f(0) = 0 So, LHL = RHL = f(0) Hence, f is continuous at π = π
