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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. (xii) ใ€–(26.57)ใ€—^(1/3) Let ๐‘ฆ=๐‘ฅ^( 1/3) where ๐‘ฅ=27 & โˆ† ๐‘ฅ=โˆ’0. 43 Now, ๐‘ฆ=๐‘ฅ^( 1/3) Differentiating w.r.t.๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=๐‘‘(๐‘ฅ^( 1/3) )/๐‘‘๐‘ฅ=1/3 ๐‘ฅ^( 1/3 โˆ’ 1)=1/3 ๐‘ฅ^( (โˆ’ 2)/( 3))=1/(3 ๐‘ฅ^( 2/( 3)) ) Using โˆ†๐‘ฆ=๐‘‘๐‘ฆ/๐‘‘๐‘ฅ โˆ†๐‘ฅ โˆ†๐‘ฆ=1/(3 ๐‘ฅ^( 2/( 3)) ) ร— โˆ†๐‘ฅ Putting Values โˆ†๐‘ฆ=1/(3 (27)^( 2/( 3)) ) ร— (โˆ’0. 43) โˆ†๐‘ฆ=(โˆ’0. 43)/(3 ร— 3^(3 ร— 2/( 3)) ) โˆ†๐‘ฆ=(โˆ’0. 43)/(3 ร— 3^2 ) โˆ†๐‘ฆ=(โˆ’0. 43)/(3 ร— 9) โˆ†๐‘ฆ=(โˆ’0. 43)/27 โˆ†๐‘ฆ=โˆ’0. 015926 We know that โˆ†๐‘ฆ=๐‘“(๐‘ฅ+โˆ†๐‘ฅ)โˆ’๐‘“(๐‘ฅ) So, โˆ†๐‘ฆ=ใ€–(๐‘ฅ+โˆ†๐‘ฅ) ใ€—^(1/3)โˆ’๐‘ฅ^( 1/3) Putting Values โˆ’0. 015926=(27+(โˆ’0. 43))^( 1/3)โˆ’(27)^( 1/3) โˆ’0. 015926=(26. 57)^( 1/3)โˆ’(27)^( 3 ร— 1/3) โˆ’0. 015926=(26. 57)^( 1/3)โˆ’3 โˆ’0. 015926+3=(26. 53)^( 1/3) 2. 984=(26. 53)^( 1/3) Thus, the Approximate Values of (26. 53)^( 1/3) is 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.