Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

Ex 5.1

Ex 5.1 ,1

Ex 5.1 ,2

Ex 5.1, 3 (a)

Ex 5.1, 3 (b)

Ex 5.1, 3 (c) Important

Ex 5.1, 3 (d) Important

Ex 5.1 ,4

Ex 5.1 ,5 Important

Ex 5.1 ,6

Ex 5.1 ,7 Important

Ex 5.1 ,8

Ex 5.1, 9 Important

Ex 5.1, 10

Ex 5.1, 11

Ex 5.1, 12 Important

Ex 5.1, 13

Ex 5.1, 14

Ex 5.1, 15 Important

Ex 5.1, 16

Ex 5.1, 17 Important

Ex 5.1, 18 Important

Ex 5.1, 19 Important

Ex 5.1, 20

Ex 5.1, 21 You are here

Ex 5.1, 22 (i) Important

Ex 5.1, 22 (ii)

Ex 5.1, 22 (iii)

Ex 5.1, 22 (iv) Important

Ex 5.1, 23

Ex 5.1, 24 Important

Ex 5.1, 25

Ex 5.1, 26 Important

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

Last updated at May 29, 2023 by Teachoo

Ex 5.1, 21 Discuss the continuity of the following functions: (a) 𝑓 (𝑥) = sin𝑥+cos𝑥 𝑓 (𝑥) = sin𝑥+cos𝑥 Let 𝑝(𝑥)=sin𝑥 & 𝑞(𝑥)=cos𝑥" " We know that sin𝑥 & cos𝑥 both continuous function ∴ 𝒑(𝒙) & 𝒒(𝒙) is continuous at all real number By Algebra of continuous function If 𝑝(𝑥)" & " 𝑞(𝑥) are continuous for all real numbers then 𝑓(𝑥)= 𝒑(𝒙)+𝒒(𝒙) is continuous for all real numbers ∴ 𝒇(𝒙) = sin𝑥+𝑐𝑜𝑠𝑥 continuous for all real numbers Ex 5.1, 21 Discuss the continuity of the following functions: (b) 𝑓(𝑥) = sin𝑥 – cos𝑥 𝑓(𝑥)= sin𝑥 – cos𝑥 Let 𝑝(𝑥)=sin𝑥 & 𝑞(𝑥)=cos𝑥" " We know that sin𝑥 & cos𝑥 are both continuous function ∴ 𝒑(𝒙) & 𝒒(𝒙) is continuous at all real number By Algebra of continuous function If 𝑝(𝑥)" & " 𝑞(𝑥) are continuous for all real numbers then 𝑓(𝑥)= 𝒑(𝒙)−𝒒(𝒙) is continuous for all real numbers ∴ 𝒇(𝒙) = 𝑠𝑖𝑛𝑥−𝑐𝑜𝑠𝑥 is continuous for all real numbers Ex 5.1, 21 Discuss the continuity of the following functions: (c) 𝑓(𝑥) = sin𝑥 . cos𝑥 𝑓(𝑥) = sin𝑥 . cos𝑥 Let 𝑝(𝑥)=sin𝑥 & 𝑞(𝑥)=cos𝑥" " We know that sin𝑥 & cos𝑥 are both continuous functions ∴ 𝒑(𝒙) & 𝒒(𝒙) is continuous at all real numbers By Algebra of continuous function If 𝑝(𝑥)" & " 𝑞(𝑥) are continuous for all real numbers then 𝑓(𝑥)= 𝒑(𝒙) . 𝒒(𝒙) is continuous for all real numbers ∴ 𝒇(𝒙) = 𝑠𝑖𝑛𝑥.𝑐𝑜𝑠𝑥 continuous for all real numbers