Last updated at Nov. 30, 2019 by Teachoo

Transcript

Ex 13.1, 6 Evaluate the Given limit: lim┬(x→0) ((x +1)5 −1)/x lim┬(x→0) ((x + 1)5 − 1)/x = ((0 + 1)5 −1)/0 = (15 − 1)/0 = (1 − 1)/0 = 0/0 Since it is of from 0/0 Hence, we simplify lim┬(x→0) ((x +1)5 −1)/x Putting y = x + 1 ⇒ x = y – 1 As x → 0 y → 0 + 1 y → 1 Our equation becomes lim┬(x→0) ((x +1)5 −1)/x = lim┬(y→1) (𝑦5 − 1)/(y − 1) = (𝐥𝐢𝐦)┬(𝐲→𝟏) (𝒚𝟓 − 𝟏^𝟓)/(𝐲 − 𝟏) = lim┬(y→1) (y5−15)/(y−1) = 5 × 15-1 = 5 × 14 = 5 ∴ lim┬(x→0) ((x + 1)5 − 1)/x = 5 We know that (𝑙𝑖𝑚)┬(𝑥→𝑎) ( 𝑥^𝑛 − 𝑎^𝑛)/(𝑥 − 𝑎) = nan – 1 Comparing (𝑙𝑖𝑚)┬(𝑦→1) ( 𝑦^5 − 1^5)/(𝑦 − 1) Here x = y , n = 5 , a = 1

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 You are here

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

Ex 13.1, 14 Important

Ex 13.1, 15 Important

Ex 13.1, 16

Ex 13.1, 17

Ex 13.1, 18

Ex 13.1, 19

Ex 13.1, 20

Ex 13.1, 21 Important

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 Important

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 10 years. He provides courses for Maths and Science at Teachoo.