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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. (i) โˆš25.3Let y = โˆš๐‘ฅ where x = 25 & โ–ณ x = 0.3 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) (0.3) = 1/(2โˆš25) (0.3) = 1/(2 ร— 5) ร— 0.3 = 0.3/10 = 0.03 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. 03=โˆš(25+0. 3)โˆ’โˆš25 0. 03=โˆš(25. 3)โˆ’5 0. 03+5=โˆš(25. 3) โˆš(25. 3)=5. 03 Hence, approximate value of โˆš25.3 is 5.03

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.