# Ex 5.1, 21 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

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.