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

Last updated at April 15, 2021 by

Last updated at April 15, 2021 by

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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. (vii) ใ(26)ใ^(1/3)Let ๐ฆ=(๐ฅ)^(1/3) where ๐ฅ=27 & โ๐ฅ=โ1 Now, ๐ฆ=ใ๐ฅ ใ^(1/3) Differentiating w.r.t.๐ฅ ๐๐ฆ/๐๐ฅ=๐(ใ๐ฅ ใ^(1/3) )/๐๐ฅ=1/3 ใ๐ฅ ใ^(1/3 โ 1) Using โ๐ฆ=๐๐ฆ/๐๐ฅ โ๐ฅ โ๐ฆ=1/(3ใ๐ฅ ใ^(2/( 3) ) ) โ๐ฅ Putting Values โ๐ฆ=1/(3(27)^( 2/3 ) )ร (โ1) โ๐ฆ=1/(3(3^3 )^( 2/3 ) )ร (โ1) โ๐ฆ=(โ1)/(3ใ ร 3ใ^(2 ) ) โ๐ฆ=(โ1)/(3 ร 9 ) โ๐ฆ=(โ1)/27 โ๐ฆ=โ0. 037037 We know that โ๐ฆ=๐(๐ฅ+โ๐ฅ)โ๐(๐ฅ) โ๐ฆ=ใ(๐ฅ+โ๐ฅ) ใ^(1/3)โ(๐ฅ)^( 1/3) Putting Values โ0. 037037=ใ(27+(โ1)) ใ^(1/3)โ(27)^( 1/3) โ0. 037037=ใ(26) ใ^(1/3)โ(3)^( 3 ร 1/3) โ0. 037037=ใ(26) ใ^(1/3)โ3 โ0. 037037+3=ใ(26) ใ^(1/3) 2. 9629=ใ(26) ใ^(1/3) Thus, Approximate Value of (26)^(1/3) is ๐. ๐๐๐๐ =1/3 ใ๐ฅ ใ^((โ 2)/( 3) )=1/(3ใ๐ฅ ใ^(2/( 3) ) ) โ๐ฆ=โ0. 037037 We know that โ๐ฆ=๐(๐ฅ+โ๐ฅ)โ๐(๐ฅ) โ๐ฆ=ใ(๐ฅ+โ๐ฅ) ใ^(1/3)โ(๐ฅ)^( 1/3) Putting Values โ0. 037037=ใ(27+(โ1)) ใ^(1/3)โ(27)^( 1/3) โ0. 037037=ใ(26) ใ^(1/3)โ(3)^( 3 ร 1/3) โ0. 037037=ใ(26) ใ^(1/3)โ3 โ0. 037037+3=ใ(26) ใ^(1/3) 2. 9629=ใ(26) ใ^(1/3) Thus, Approximate Value of (26)^(1/3) is ๐. ๐๐๐๐

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.