# 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

Ex 5.1

Ex 5.1 ,1

Ex 5.1 ,2

Ex 5.1 ,3

Ex 5.1 ,4

Ex 5.1 ,5

Ex 5.1 ,6

Ex 5.1 ,7

Ex 5.1 ,8

Ex 5.1, 9 Important

Ex 5.1, 10

Ex 5.1, 11

Ex 5.1, 12

Ex 5.1, 13 Important

Ex 5.1, 14

Ex 5.1, 15

Ex 5.1, 16 Important

Ex 5.1, 17

Ex 5.1, 18 Important

Ex 5.1, 19

Ex 5.1, 20

Ex 5.1, 21 You are here

Ex 5.1, 22

Ex 5.1, 23

Ex 5.1, 24

Ex 5.1, 25

Ex 5.1, 26

Ex 5.1, 27

Ex 5.1, 28 Important

Ex 5.1, 29

Ex 5.1, 30 Important

Ex 5.1, 31

Ex 5.1, 32

Ex 5.1, 33

Ex 5.1, 34 Important

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.