Last updated at May 29, 2018 by Teachoo

Transcript

Ex 13.1, 25 (Method 1) Evaluate lim x 0 f(x), where f(x) = x x 0, , x 0 x=0 Finding limit at x = 0 lim x 0 f(x) = lim x 0 + f(x) = lim x 0 f(x) Thus, lim x 0 f(x) = 1 & lim x 0 + f(x) = 1 Since 1 1 So, f(x) + f(x) So, left hand limit & right hand limit are not equal Hence, f(x) does not exist Ex13.1, 25 (Method 2) Evaluate lim x 0 f(x), where f(x) = x x 0, , x 0 x=0 We know that lim x a f(x) exist only if lim x f(x) = lim x + f(x) Similarly in this question we have find limits First we have to prove limit exists by proving lim x 0 f(x) = lim x 0 + f(x) For f(x) f(x) = x x So, as x tends to 0, f(x) tends to 1 0 f(x) = 1 For + f(x) f(x) = x x So, as x tends to 0, f(x) tends to 1 0 + f(x) = 1 Thus, lim x 0 f(x) = 1 & lim x 0 + f(x) = 1 Since 1 1 So, lim x 0 f(x) lim x 0 + f(x) So, left hand limit & right hand limit are not equal Hence, f(x) does not exist

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 You are here

Ex 13.1, 26

Ex 13.1, 27

Ex 13.1, 28 Important

Ex 13.1, 29

Ex 13.1, 30 Important

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.