Check sibling questions

Ex 13.1, 26 - Find lim x -> 0 where f(x) = { x / |x|, 0 - Teachoo

Ex 13.1, 26 - Chapter 13 Class 11 Limits and Derivatives - Part 2

Solve all your doubts with Teachoo Black (new monthly pack available now!)


Transcript

Ex 13.1, 26 (Method 1) Evaluate lim x 0 f(x), where f(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, 26 (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 So, as x tends to 0, f(x) tends to 1 0 + f(x) = 1 For f(x) f(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, f(x) + f(x) So, left hand limit & right hand limit are not equal Hence, f(x) does not exist

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.