Subscribe to our Youtube Channel - https://www.youtube.com/channel/UCZBx269Tl5Os5NHlSbVX4Kg

Last updated at Nov. 30, 2019 by Teachoo

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

Chapter 13 Class 11 Limits and Derivatives

Concept wise

- Limits - Definition
- Limits - 0/0 form
- Limits - x^n formula
- Limits - Of Trignometric functions
- Limits - Limit exists
- Derivatives by 1st principle - At a point
- Derivatives by 1st principle - At a general point
- Derivatives by formula - x^n formula
- Derivatives by formula - sin & cos
- Derivatives by formula - other trignometric

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.