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. (xi) ใ€–(0.0037)ใ€—^(1/2) Let y = โˆš๐‘ฅ Let x = 0.0036 & โ–ณ x = 0.0001 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) (0.0001) = 1/(2โˆš0.0036) (0.0001) = 1/(2 ร— 0.06) ร— (0.0001) = 0.0001/0.12 = 1/1200 = 0.000833 Also, โˆ†๐‘ฆ=๐‘“(๐‘ฅ+โˆ†๐‘ฅ)โˆ’๐‘“(๐‘ฅ) So, โˆ†๐‘ฆ=(๐‘ฅ+โˆ†๐‘ฅ)^( 1/2)โˆ’(๐‘ฅ)^( 1/2) Putting Values 0. 000833=(0. 0036+0. 0001)^( 1/2)โˆ’(0. 0036)^( 1/2) 0. 000833=(0. 0037)^( 1/2)โˆ’(36/10000)^(1/2) 0. 000833=(0. 0037)^( 1/2)โˆ’(6/100)^( 2 ร— 1/2) 0. 000833=(0. 0037)^( 1/2)โˆ’(0. 06)^(2 ร— 1/2 ) 0. 000833=(0. 0037)^( 1/2)โˆ’(0. 06) 0. 000833+0. 06=(0. 0037)^( 1/2) 0. 060833=(0. 0037)^( 1/2) (0. 0037)^( 1/2)=0. 060833 Thus, the Approximate Value of (0. 0037)^( 1/2)=๐ŸŽ. ๐ŸŽ๐Ÿ”๐ŸŽ๐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.