Check Full Chapter Explained - Continuity and Differentiability - Continuity and Differentiability Class 12

Last updated at Dec. 8, 2016 by Teachoo

Check Full Chapter Explained - Continuity and Differentiability - Continuity and Differentiability Class 12

Transcript

Ex 5.1, 21 Discuss the continuity of the following functions: (a) π (π₯) = sinβ‘π₯+cosβ‘π₯ π (π₯) = sinβ‘π₯+cosβ‘π₯ Let π(π₯)=sinβ‘π₯ & π(π₯)=cosβ‘π₯" " We know that sinβ‘π₯ & cosβ‘π₯ both continuous function β π(π₯) & π(π₯) is continuous at all real number By Algebra of continuous function If π(π₯)" & " π(π₯) are continuous for all real numbers then π(π₯)= π(π₯)+π(π₯) is continuous for all real numbers β΄ π(π) = π¬π’π§β‘π+πππβ‘π continuous for all real numbers Ex 5.1, 21 Discuss the continuity of the following functions: (b) π (π₯) = sinβ‘π₯ β cosβ‘π₯ π (π₯) = sinβ‘π₯ β cosβ‘π₯ Let π(π₯)=sinβ‘π₯ & π(π₯)=cosβ‘π₯" " We know that sinβ‘π₯ & cosβ‘π₯ are both continuous function β π(π₯) & π(π₯) is continuous at all real number By Algebra of continuous function If π(π₯)" & " π(π₯) are continuous for all real numbers then π(π₯)= π(π₯)βπ(π₯) is continuous for all real numbers β΄ π(π) = πππβ‘πβπππβ‘π is continuous for all real numbers Ex 5.1, 21 Discuss the continuity of the following functions: (c) π (π₯) = sinβ‘π₯ . cosβ‘π₯ π (π₯) = sinβ‘π₯ . cosβ‘π₯ Let π(π₯)=sinβ‘π₯ & π(π₯)=cosβ‘π₯" " We know that sinβ‘π₯ & cosβ‘π₯ are both continuous functions β π(π₯) & π(π₯) is continuous at all real numbers By Algebra of continuous function If π(π₯)" & " π(π₯) are continuous for all real numbers then π(π₯)= π(π₯) . π(π₯) is continuous for all real numbers β΄ π(π) = πππβ‘π.πππβ‘π continuous for all real numbers

Algebra of continous 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

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.