# Ex 5.1, 13 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Ex 5.1, 13 Is the function defined by ๐ ๐ฅ๏ทฏ= ๐ฅ+5, ๐๐ ๐ฅโค1๏ทฎ& ๐ฅโ5 , ๐๐ ๐ฅ>1๏ทฏ๏ทฏ a continuous function? Given function is , ๐ ๐ฅ๏ทฏ= ๐ฅ+5, ๐๐ ๐ฅโค1๏ทฎ& ๐ฅโ5 , ๐๐ ๐ฅ>1๏ทฏ๏ทฏ Case 1 At x = 1 f is continuous at x = 1 if L.H.L = R.H.L = ๐ 1๏ทฏ i.e. if lim๏ทฎxโ 1๏ทฎโ๏ทฏ๏ทฏ ๐ ๐ฅ๏ทฏ = lim๏ทฎxโ 1๏ทฎ+๏ทฏ๏ทฏ ๐ ๐ฅ๏ทฏ = ๐ 1๏ทฏ Thus, L.H.L โ R.H.L โ f is discontinuous at ๐ =๐ Case 2 Let x = c , where c < 1 ๐ ๐ฅ๏ทฏ=๐ฅ+5 f is continuous at x = c if if lim๏ทฎxโ๐๏ทฏ ๐ ๐ฅ๏ทฏ=๐(๐) Thus, lim๏ทฎxโ๐๏ทฏ ๐ ๐ฅ๏ทฏ=๐ ๐๏ทฏ โ f is continuous for ๐ฅ =๐ less than 1. โ f is at continuous for all real numbers less than 1. Case 3 Let x = c (where c > 1) ๐ ๐ฅ๏ทฏ= ๐ฅโ5 f is continuous at x = c if lim๏ทฎxโ๐๏ทฏ ๐ ๐ฅ๏ทฏ=๐(๐) Thus lim๏ทฎxโ๐๏ทฏ ๐ ๐ฅ๏ทฏ=๐(๐) โ f is continuous for ๐ฅ =๐ ( c is greater than 1) โ f is continuous at all real numbers greater than 1. Hence, only x = 1 is point of discontinuity. โ f is continuous at all real point. Thus, f is continuous for all ๐โ๐โ{๐}.

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 You are here

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

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 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.