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

Last updated at April 15, 2021 by Teachoo

Last updated at April 15, 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. (iv) ใ(0.009)ใ^(1/3)Let ๐ฆ=(๐ฅ)^(1/3) where ๐ฅ=0. 008 & โ๐ฅ=0. 001 Differentiating w.r.t.๐ฅ ๐๐ฆ/๐๐ฅ=๐(ใ๐ฅ ใ^(1/3) )/๐๐ฅ=1/3 ๐ฅ^((โ2)/3)=1/(3ใ ๐ฅใ^( 2/3) ) Using โ๐ฆ=๐๐ฆ/๐๐ฅ โ๐ฅ โ๐ฆ=1/(3ใ ๐ฅใ^( 2/3) ) รโ๐ฅ Putting Values โ๐ฆ=1/(3(0. 008)^( 2/3) ) ร0. 001 โ๐ฆ=(0. 001)/(3(8/1000)^(2/3) ) โ๐ฆ=(0. 001)/(3(2/10)^( 3 ร 2/3) ) โ๐ฆ=(0. 001)/(3(2/10)^2 ) โ๐ฆ=(0. 001)/(3 ร 4/100) โ๐ฆ=(0.001 ร 100)/12 โ๐ฆ=0. 008 We know that โ๐ฆ=๐(๐ฅ+โ๐ฅ)โ๐(๐ฅ) โ๐ฆ=ใ(๐ฅ+โ๐ฅ) ใ^(1/3)โใ๐ฅ ใ^(1/3) Putting Values 0. 008=(0. 008" " +0. 001)^( 1/3)โ(0. 008" " )^( 1/3) 0. 008=(0. 009)^( 1/3)โ(0. 008)^( 1/3) 0. 008=(0. 009)^( 1/3)โ(8/1000)^( 1/3) 0. 008=(0. 009)^( 1/3)โ(2/10)^( 3 ร 1/3) 0. 008=(0. 009)^( 1/3)โ(2/10) 0. 008=(0. 009)^( 1/3)โ0. 2 0. 008+0. 2=(0. 009)^( 1/3) (0. 009)^( 1/3)=0. 208 Thus , Approximate Value of (0 . 009)^(1/3) is ๐. ๐๐๐

Ex 6.4

Ex 6.4, 1 (i)
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Chapter 6 Class 12 Application of Derivatives

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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.