Last updated at May 29, 2018 by Teachoo

Transcript

Ex 13.1, 30 If f(x) = x +1, x<0 0 x=0 x 1, x>0 . For what value (s) of a does f(x) exists? We need to find value of a for which lim x a f(x) exists lim x a f(x) exists only if lim x a + f (x) = lim x a f(x) We check limit different values of a When a = 0 When a < 0 When a > 0 Case 1: When a = 0 Limit exists at a = 0 if lim x 0 + f(x) = lim x 0 f(x) f(x) = x +1, x<0 0 x=0 x 1, x>0 . Since 1 1 lim x 0 f(x) lim x 0 + f(x) So, left hand limit and right hand limit are not equal at x = 0 Hence lim x 0 f(x) does not exists At x = 0 Limit does not exists Case 2: When x = a, a > 0 Limit exists at a if lim x + f(x) = lim x f(x) f(x) = x +1, x<0 0 x=0 x 1, x>0 . Since lim x f(x) = lim x + f(x) Hence at all point x = a, a > 0 f(x) exists Case 3: When x = a, a < 0 Limit exists at a if lim x + f(x) = lim x f(x) f(x) = x +1, x<0 0 x=0 x 1, x>0 . Since lim x f(x) = lim x + f(x) Hence at all point x = a, a < 0 f(x) exists f(x) exists exists for all a 0

Ex 13.1

Ex 13.1, 1

Ex 13.1, 2

Ex 13.1, 3

Ex 13.1, 4

Ex 13.1, 5

Ex 13.1, 6 Important

Ex 13.1, 7

Ex 13.1, 8

Ex 13.1, 9

Ex 13.1,10 Important

Ex 13.1, 11

Ex 13.1, 12

Ex 13.1, 13 Important

Ex 13.1, 14

Ex 13.1, 15

Ex 13.1, 16 Important

Ex 13.1, 17

Ex 13.1, 18

Ex 13.1, 19

Ex 13.1, 20

Ex 13.1, 21

Ex 13.1, 22 Important

Ex 13.1, 23

Ex 13.1, 24

Ex 13.1, 25 Important

Ex 13.1, 26

Ex 13.1, 27

Ex 13.1, 28 Important

Ex 13.1, 29

Ex 13.1, 30 Important You are here

Ex 13.1, 31

Ex 13.1, 32 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.