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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. (viii) ใ€–(255)ใ€—^(1/4) Let ๐‘ฆ=(๐‘ฅ)^(1/4) where ๐‘ฅ=256 & โˆ†๐‘ฅ=โˆ’1 Now, ๐‘ฆ=(๐‘ฅ)^(1/4) Differentiating w.r.t.๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=๐‘‘(ใ€–๐‘ฅ ใ€—^(1/4) )/๐‘‘๐‘ฅ=1/4 ๐‘ฅ^( 1/4 โˆ’ 1) =1/4 ๐‘ฅ^( (โˆ’3)/( 4))=1/(4 ๐‘ฅ^( 3/( 4)) ) Using โˆ†๐‘ฆ=๐‘‘๐‘ฆ/๐‘‘๐‘ฅ โˆ†๐‘ฅ โˆ†๐‘ฆ=1/(4ใ€– ๐‘ฅใ€—^( 3/( 4)) ) ร—โˆ†๐‘ฅ Putting Values โˆ†๐‘ฆ=1/(4 (256)^(3/4) ) ร— (โˆ’1) โˆ†๐‘ฆ=(โˆ’ 1)/(4 (4^4 )^(3/4) ) โˆ†๐‘ฆ=(โˆ’ 1)/(4 ร— 4^3 ) โˆ†๐‘ฆ=(โˆ’ 1)/(4 ร— 64) โˆ†๐‘ฆ=(โˆ’ 1)/256 โˆ†๐‘ฆ=โˆ’0. 0039 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€—^(1/4)โˆ’๐‘ฅ^( 1/4) Putting Values โˆ’0. 0039=ใ€–(256+(โˆ’1)) ใ€—^(1/4)โˆ’(256)^( 1/4) โˆ’0. 0039=ใ€–(255) ใ€—^(1/4)โˆ’(4^4 )^( 1/4) โˆ’0. 0039=ใ€–(255) ใ€—^(1/4)โˆ’4 โˆ’0. 0039=ใ€–(255) ใ€—^(1/4)โˆ’4 โˆ’0. 0039+4=ใ€–(255) ใ€—^(1/4) 3. 9961=ใ€–(255) ใ€—^(1/4) Thus, the Approximate Values of ใ€–(255) ใ€—^(1/4) 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.