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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. (iii) โˆš0.6 Let y = โˆš๐‘ฅ where x = 0.64 & โ–ณx = โ€“0.04 Since y = โˆš๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = (๐‘‘(โˆš๐‘ฅ))/๐‘‘๐‘ฅ = 1/(2โˆš๐‘ฅ) Now, โˆ†๐‘ฆ = ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ โ–ณx = 1/(2โˆš0.64) (โ€“0.04) = 1/(2โˆš(64/100)) (โ€“0.04) = 1/(2 ร—8/10) ร— (โ€“0.04) = (โˆ’10 ร— 0.04)/16 = (โˆ’10 ร— 4)/(16 ร— 100) = โ€“0.025 Also, โˆ†๐‘ฆ=๐‘“(๐‘ฅ+โˆ†๐‘ฅ)โˆ’๐‘“(๐‘ฅ) Putting values โˆ†๐‘ฆ=โˆš(๐‘ฅ+โˆ†๐‘ฅ)โˆ’โˆš๐‘ฅ โˆ’0. 025=โˆš(0.64โˆ’0.04)โˆ’โˆš0.64 โˆ’0.025=โˆš0.60โˆ’0.8 0.8 โ€“ 0. 025=โˆš0.60 โˆš0.60=0.775 Hence, approximate value of โˆš0.60 is 0.775

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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.