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Example 19 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at June 2, 2023 by Teachoo
Continuity of composite functions
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 19 Show that the function defined by f (x) = sin (x2) is a continuous function.Given π(π₯) = sinβ‘(π₯^2 ) Let π(π) = sinβ‘π₯ & π(π) = π₯^2 Now, (π π π)(π) = g(β(π₯)) = π(π₯^2 ) = sinβ‘(π₯^2 ) = π(π) So, we can write π(π₯) = ππβ Here, π(π₯) = sinβ‘π₯ is continuous & β(π₯) = π₯^2 is continuous being a polynomial . We know that if two function π & β are continuous then their composition πππ is continuous Hence, ππβ(π₯) is continuous β΄ π(π) is continuous .
