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

Last updated at April 15, 2021 by Teachoo

Last updated at April 15, 2021 by Teachoo

Transcript

Ex 6.4, 1 Using differentials, find the approximate value of each of the following up to 3 places of decimal. (xii) ใ(26.57)ใ^(1/3)Let ๐ฆ=๐ฅ^( 1/3) where ๐ฅ=27 & โ ๐ฅ=โ0. 43 Now, ๐ฆ=๐ฅ^( 1/3) Differentiating w.r.t.๐ฅ ๐๐ฆ/๐๐ฅ=๐(๐ฅ^( 1/3) )/๐๐ฅ=1/3 ๐ฅ^( 1/3 โ 1)=1/3 ๐ฅ^( (โ 2)/( 3))=1/(3 ๐ฅ^( 2/( 3)) ) Using โ๐ฆ=๐๐ฆ/๐๐ฅ โ๐ฅ โ๐ฆ=1/(3 ๐ฅ^( 2/( 3)) ) ร โ๐ฅ Putting Values โ๐ฆ=1/(3 (27)^( 2/( 3)) ) ร (โ0. 43) โ๐ฆ=(โ0. 43)/(3 ร 3^(3 ร 2/( 3)) ) โ๐ฆ=(โ0. 43)/(3 ร 3^2 ) โ๐ฆ=(โ0. 43)/(3 ร 9) โ๐ฆ=(โ0. 43)/27 โ๐ฆ=โ0. 015926 We know that โ๐ฆ=๐(๐ฅ+โ๐ฅ)โ๐(๐ฅ) So, โ๐ฆ=ใ(๐ฅ+โ๐ฅ) ใ^(1/3)โ๐ฅ^( 1/3) Putting Values โ0. 015926=(27+(โ0. 43))^( 1/3)โ(27)^( 1/3) โ0. 015926=(26. 57)^( 1/3)โ(27)^( 3 ร 1/3) โ0. 015926=(26. 57)^( 1/3)โ3 โ0. 015926+3=(26. 53)^( 1/3) 2. 984=(26. 53)^( 1/3) Thus, the Approximate Values of (26. 53)^( 1/3) 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.