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, 32 Show that the function defined by 𝑓 𝑥= cos𝑥 is a continuous function. 𝑓(𝑥) = cos𝑥 Let 𝑔(𝑥) = 𝑥 & ℎ 𝑥 = cos𝑥 𝑔𝑜ℎ 𝑥 = g ℎ 𝑥 = 𝑔 cos𝑥 = cos𝑥 = 𝑓 𝑥 Hence 𝑓 𝑥 = 𝑔𝑜ℎ 𝑥 We know that, h(x) = cos𝑥 is continuous & g (x) = 𝑥 is continuous as it is a modulus function We know that If two function 𝑔 𝑥 & ℎ 𝑥 both continuous then their composition is also continuous ∴ 𝑔𝑜ℎ 𝑥 is continuous Thus, 𝒇 𝒙 is continuous for all real values.

Ex 5.1

Ex 5.1 ,1

Ex 5.1 ,2

Ex 5.1 ,3 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

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

Ex 5.1, 22

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 You are here

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.