Check Full Chapter Explained - Continuity and Differentiability - Application of Derivatives (AOD) Class 12

 

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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. (xiv) ใ€–(3.968)ใ€—^(3/2) Let ๐‘ฆ=๐‘ฅ^( 3/2) where ๐‘ฅ=4 & โˆ†๐‘ฅ=โˆ’0. 032 Now, ๐‘ฆ=๐‘ฅ^( 3/2) Differentiating w.r.t.๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=๐‘‘(๐‘ฅ^( 3/2) )/๐‘‘๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=3/2 ใ€–๐‘ฅ ใ€—^(1/2) Using โˆ†๐‘ฆ=๐‘‘๐‘ฆ/๐‘‘๐‘ฅ โˆ†๐‘ฅ โˆ†๐‘ฆ=3/2 ๐‘ฅ^( 1/2) โˆ†๐‘ฅ Putting Values โˆ†๐‘ฆ=3/2 (4)^( 1/2) . (โˆ’0. 032) โˆ†๐‘ฆ=3/2 (2^2 )^( 1/2) . (โˆ’0. 032) โˆ†๐‘ฆ=3/2 ร— 2 ร— (โˆ’0. 032) โˆ†๐‘ฆ=3 ร— (โˆ’0. 032) โˆ†๐‘ฆ=โˆ’0. 096 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)^( 3/2)โˆ’๐‘ฅ^( 3/2) Putting Values โˆ’0. 096=(4+(โˆ’0. 032))^( 3/2)โˆ’(4)^( 3/2) โˆ’0. 096=(4โˆ’0. 032)^( 3/2)โˆ’ใ€–(2)^2ใ€—^( ร— 3/2) โˆ’0. 096=(3. 968)^( 3/2)โˆ’2^3 โˆ’0. 096=(3. 968)^( 3/2)โˆ’8 โˆ’0. 096+8=(3. 968)^( 3/2) 7. 904=(3. 968)^( 3/2) (3. 968)^( 3/2)=7.904 Thus, Approximate Values of (3. 968)^( 3/2) is ๐Ÿ•. ๐Ÿ—๐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.