# Ex 6.4, 1 (xiv) - Chapter 6 Class 12 Application of Derivatives (Term 1)

Last updated at Aug. 19, 2021 by Teachoo

Last updated at Aug. 19, 2021 by Teachoo

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Ex 6.4, 1 Using differentials, find the approximate value of each of the following up to 3 places of decimal. (xiv) ใ(3.968)ใ^(3/2)Let ๐ฆ=๐ฅ^( 3/2) where ๐ฅ=4 & โ๐ฅ=โ0. 032 Now, ๐ฆ=๐ฅ^( 3/2) Differentiating w.r.t.๐ฅ ๐๐ฆ/๐๐ฅ=๐(๐ฅ^( 3/2) )/๐๐ฅ ๐๐ฆ/๐๐ฅ=3/2 ใ๐ฅ ใ^(1/2) Using โ๐ฆ=๐๐ฆ/๐๐ฅ โ๐ฅ โ๐ฆ=3/2 ๐ฅ^( 1/2) โ๐ฅ Putting Values โ๐ฆ=3/2 (4)^( 1/2) . (โ0. 032) โ๐ฆ=3/2 (2^2 )^( 1/2) . (โ0. 032) โ๐ฆ=3/2 ร 2 ร (โ0. 032) โ๐ฆ=3 ร (โ0. 032) โ๐ฆ=โ0. 096 We know that โ๐ฆ=๐(๐ฅ+โ๐ฅ)โ๐(๐ฅ) So, โ๐ฆ=(๐ฅ+โ๐ฅ)^( 3/2)โ๐ฅ^( 3/2) Putting Values โ0. 096=(4+(โ0. 032))^( 3/2)โ(4)^( 3/2) โ0. 096=(4โ0. 032)^( 3/2)โใ(2)^2ใ^( ร 3/2) โ0. 096=(3. 968)^( 3/2)โ2^3 โ0. 096=(3. 968)^( 3/2)โ8 โ0. 096+8=(3. 968)^( 3/2) 7. 904=(3. 968)^( 3/2) (3. 968)^( 3/2)=7.904 Thus, Approximate Values of (3. 968)^( 3/2) is ๐. ๐๐๐

Ex 6.4

Ex 6.4, 1 (i)
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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.