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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. (v) ใ€–(0.999)ใ€—^(1/10) Let ๐‘ฆ=ใ€–๐‘ฅ ใ€—^(1/10) where ๐‘ฅ=1 , โˆ†๐‘ฅ=โˆ’0. 001 Now, ๐‘ฆ=๐‘ฅ^( 1/10) Differentiating w.r.t.๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=๐‘‘(๐‘ฅ^( 1/10) )/๐‘‘๐‘ฅ=1/10 ๐‘ฅ^((โˆ’9)/10)=1/(10ใ€– ๐‘ฅใ€—^(9/10) ) Using โˆ†๐‘ฆ=๐‘‘๐‘ฆ/๐‘‘๐‘ฅ โˆ†๐‘ฅ Putting Values โˆ†๐‘ฆ= 1/(10ใ€– ๐‘ฅใ€—^(9/10) ) โˆ†๐‘ฅ โˆ†๐‘ฆ= 1/(10 (1)^(9/10) ) ร— (โˆ’0. 001) โˆ†๐‘ฆ= 1/10 ร—(โˆ’0. 001) โˆ†๐‘ฆ=โˆ’0. 0001 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€—^(1/10)โˆ’๐‘ฅ^( 1/10) Putting Values โˆ†๐‘ฆ=(1+(โˆ’0. 001))^(1/10)โˆ’(1)^(1/10) โˆ’0. 0001=(0. 999)^(1/10)โˆ’1 โˆ’0. 0001+1=(0. 999)^(1/10) 0. 9999=(0. 999)^(1/10) Thus, the Approximate Value of (0. 999)^(1/10) is ๐ŸŽ. 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.