Last updated at Dec. 8, 2016 by Teachoo

Transcript

Ex 13.1, 23 (Method 1) Find lim x 0 f(x) and lim x 1 f(x), where f(x) = 2x+3. 3 x+1 , x 0 x>0 Finding limit at x = 0 lim x 0 f(x) = lim x 0 + f(x) = lim x 0 f(x) f(x) = f(x) = f(x) = 3 f(x) = 2x+3. 3 x+1 , x 0 x>0 Finding limit at x = 1 lim x 1 f(x) = lim x 1 + f(x) = lim x 1 f(x) f(x) = f(x) = + f(x) = 6 Ex 13.1, 23 (Method 2) Find lim x 0 f(x) and lim x 1 f(x), where f(x) = 2x+3. 3 x+1 , x 0 x>0 Finding limit at x = 0 We know that lim x f(x) exists only if Left Hand limit = Right hand limit i.e. lim x f(x) = lim x + f(x) Similarly in question , we have to find limits First we have to prove lim x 0 f(x) = lim x 0 + f(x) For f(x) , f(x) = 2x + 3 Hence if we move value of x towards 0, value of f(x) tends towards 3 Hence, lim x 0 f(x) = 3 For + f(x) , f(x) = 3(x + 1) When we move value of x toward 0 value of f(x) tends to 3 Hence , lim x 0 + f(x) = 3 Thus lim x 0 f(x) = lim x 0 + f(x) = 3 Hence limit exists Thus, f(x) = f(x) = + f(x) = 3 f(x) = 2x+3. 3 x+1 , x 0 x>0 Finding limit at x = 1 lim x 1 f(x) = lim x 1 + f(x) = lim x 1 f(x) f(x) = f(x) = + f(x) = 6

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 Important

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 Important

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 Important

Ex 13.1, 21

Ex 13.1, 22 Important

Ex 13.1, 23 You are here

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

Ex 13.1, 31 Important

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.