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  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. (vii) ใ€–(26)ใ€—^(1/3) Let ๐‘ฆ=(๐‘ฅ)^(1/3) where ๐‘ฅ=27 & โˆ†๐‘ฅ=โˆ’1 Now, ๐‘ฆ=ใ€–๐‘ฅ ใ€—^(1/3) Differentiating w.r.t.๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=๐‘‘(ใ€–๐‘ฅ ใ€—^(1/3) )/๐‘‘๐‘ฅ=1/3 ใ€–๐‘ฅ ใ€—^(1/3 โˆ’ 1) =1/3 ใ€–๐‘ฅ ใ€—^((โˆ’ 2)/( 3) )=1/(3ใ€–๐‘ฅ ใ€—^(2/( 3) ) ) Using โˆ†๐‘ฆ=๐‘‘๐‘ฆ/๐‘‘๐‘ฅ โˆ†๐‘ฅ โˆ†๐‘ฆ=1/(3ใ€–๐‘ฅ ใ€—^(2/( 3) ) ) โˆ†๐‘ฅ Putting Values โˆ†๐‘ฆ=1/(3(27)^( 2/3 ) )ร— (โˆ’1) โˆ†๐‘ฆ=1/(3(3^3 )^( 2/3 ) )ร— (โˆ’1) โˆ†๐‘ฆ=(โˆ’1)/(3ใ€– ร— 3ใ€—^(2 ) ) โˆ†๐‘ฆ=(โˆ’1)/(3 ร— 9 ) โˆ†๐‘ฆ=(โˆ’1)/27 โˆ†๐‘ฆ=โˆ’0. 037037 We know that โˆ†๐‘ฆ=๐‘“(๐‘ฅ+โˆ†๐‘ฅ)โˆ’๐‘“(๐‘ฅ) โˆ†๐‘ฆ=ใ€–(๐‘ฅ+โˆ†๐‘ฅ) ใ€—^(1/3)โˆ’(๐‘ฅ)^( 1/3) Putting Values โˆ’0. 037037=ใ€–(27+(โˆ’1)) ใ€—^(1/3)โˆ’(27)^( 1/3) โˆ’0. 037037=ใ€–(26) ใ€—^(1/3)โˆ’(3)^( 3 ร— 1/3) โˆ’0. 037037=ใ€–(26) ใ€—^(1/3)โˆ’3 โˆ’0. 037037+3=ใ€–(26) ใ€—^(1/3) 2. 9629=ใ€–(26) ใ€—^(1/3) Thus, Approximate Value of (26)^(1/3) is ๐Ÿ. ๐Ÿ—๐Ÿ”๐Ÿ๐Ÿ—

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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.