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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. (ii) โˆš49.5 Let y = โˆš๐‘ฅ where x = 49 & โ–ณ x = 0.5 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/(2โˆš๐‘ฅ) (0.5) = 1/(2 ร— โˆš49) ร— 0.5 = 1/(2 ร— 7) ร— 0.5 = 0.5/14 = 0.036 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 0. 036=โˆš(49+0. 5)โˆ’โˆš49 0. 036=โˆš49.5โˆ’7 0. 036+7=โˆš49.5 โˆš49.5=7. 036 Hence, approximate value of โˆš49.5 is 7.036

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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.