# Ex 5.1 ,1

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Ex 5.1, 1 Prove that the function ๐ (๐ฅ) = 5๐ฅ โ 3 is continuous at ๐ฅ = 0, at ๐ฅ = โ 3 and at ๐ฅ = 5 Given ๐ (๐ฅ) = 5๐ฅ โ 3 (i) At ๐=๐ f is continuous at x = 0 if ๏ท๐ฅ๐ข๐ฆ๏ทฎ๐ฑโ๐๏ทฏ ๐(๐) = ๐(๐) Since, L.H.S = R.H.S โด ๏ทlim๏ทฎxโ0๏ทฏ ๐(๐ฅ) = ๐(0) Hence, f is continuous at ๐ = ๐ (ii) At x = โ3 f is continuous at x = โ3 if ๏ท lim๏ทฎxโโ3๏ทฏ ๐๏ท๐ฅ๏ทฏ= ๐๏ทโ3๏ทฏ Since, L.H.S = R.H.S โด ๏ทlim๏ทฎxโโ3๏ทฏ ๐(๐ฅ) = ๐(โ3) Hence, f is continuous at ๐ =โ3 (iii) At ๐ =๐ f is continuous at x = 5 if ๏ท lim๏ทฎxโ5๏ทฏ ๐๏ท๐ฅ๏ทฏ= ๐๏ท5๏ทฏ Since, L.H.S = R.H.S โด ๏ท lim๏ทฎxโ5๏ทฏ ๐๏ท๐ฅ๏ทฏ= ๐๏ท5๏ทฏ Hence, f is continuous at ๐ =๐ Thus the function is continuous at ๐ =๐, at ๐ =โ๐ & at ๐ =๐

Ex 5.1 ,1
You are here

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

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 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.