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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. (ix) ใ€–(82)ใ€—^(1/4) Let ๐‘ฆ=(๐‘ฅ)^( 1/4) where ๐‘ฅ=81 โˆ†๐‘ฅ=1 Now, ๐‘ฆ=(๐‘ฅ)^( 1/4) Differentiating w.r.t.๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=๐‘‘(๐‘ฅ^( 1/4) )/๐‘‘๐‘ฅ=1/4 ใ€–๐‘ฅ ใ€—^(1/4 โˆ’ 1)=1/4 ใ€–๐‘ฅ ใ€—^((โˆ’3)/( 4))=1/(4ใ€–๐‘ฅ ใ€—^(3/4) ) Using โˆ†๐‘ฆ=๐‘‘๐‘ฆ/๐‘‘๐‘ฅ โˆ†๐‘ฅ โˆ†๐‘ฆ=1/(4ใ€– ๐‘ฅ ใ€—^(3/4) ) โˆ†๐‘ฆ Putting Values โˆ†๐‘ฆ=1/(4(81)^( 3/4) ) ร— (1) โˆ†๐‘ฆ=1/(4 ร—3^(4 ร— 3/4 ) ) ร— (1) โˆ†๐‘ฆ=1/(4 ร— 3^3 ) โˆ†๐‘ฆ=1/(4 ร—27) โˆ†๐‘ฆ=1/108 โˆ†๐‘ฆ=0. 009 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)^( 1/4) โˆ’(๐‘ฅ)^( 1/4) Putting Values 0. 009=(81+1)^( 1/4)โˆ’ใ€–(81) ใ€—^(1/4) 0. 009=(82)^( 1/4)โˆ’(3)^(4 ร— 1/4 ) 0. 009=(82)^( 1/4)โˆ’3 0. 009+3=(82)^( 1/4) 3. 009=(82)^( 1/4) Thus, the Approximate Value of (82)^( 1/4) is ๐Ÿ‘. ๐ŸŽ๐ŸŽ๐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.