Slide31.JPG

Slide32.JPG
Slide33.JPG Slide34.JPG

  1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise

Transcript

Ex 6.4, 1 Using differentials, find the approximate value of each of the following up to 3 places of decimal. (x) ใ€–(401)ใ€—^(1/2) Let ๐‘ฆ=๐‘ฅ^( 1/2) where ๐‘ฅ=400 & โˆ†๐‘ฅ=1 Now, ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=1/(2โˆš๐‘ฅ) Using โˆ†๐‘ฆ=๐‘‘๐‘ฆ/๐‘‘๐‘ฅ โˆ†๐‘ฅ โˆ†๐‘ฆ=๐‘‘๐‘ฆ/(2โˆš๐‘ฅ) โˆ†๐‘ฅ Putting Values โˆ†๐‘ฆ=1/(2โˆš400) ร—(1) โˆ†๐‘ฆ=1/(2โˆš400) ร—(1) โˆ†๐‘ฆ=1/(2โˆš(ใ€–20ใ€—^2 )) โˆ†๐‘ฆ=1/(2 ร— 20) โˆ†๐‘ฆ=1/40 โˆ†๐‘ฆ=0. 025 We know that โˆ†๐‘ฆ=๐‘“(๐‘ฅ+โˆ†๐‘ฅ)โˆ’๐‘“(๐‘ฅ) So, โˆ†๐‘ฆ= (๐‘ฅ+โˆ†๐‘ฅ)^( 1/2)โˆ’(๐‘ฅ)^( 1/2) Putting Values 0. 025=(400+1)^( 1/(2 ))โˆ’ใ€–(400) ใ€—^(1/2) 0. 025=(401)^( 1/2)โˆ’(20)^( 2 ร— 1/2) 0. 025=(401)^( 1/2)โˆ’20 0. 025+20=(401)^( 1/2) 20. 025=(401)^( 1/2) (401)^( 1/2)=20. 025 Thus, the Approximate Value of (401)^( 1/2) is ๐Ÿ๐ŸŽ. ๐ŸŽ๐Ÿ๐Ÿ“

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
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.