# Ex 6.4, 1 (vi) - 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. (vi) ใ(15)ใ^(1/4)Let ๐ฆ=ใ๐ฅ ใ^(1/4) where ๐ฅ=16 , โ๐ฅ=โ1 Now, ๐ฆ=๐ฅ^( 1/4) Differentiating w.r.t.๐ฅ ๐๐ฆ/๐๐ฅ=๐(๐ฅ^( 1/4) )/๐๐ฅ=1/4 ๐ฅ^( (1 โ 4)/4 )=1/4 ๐ฅ^( (โ3)/( 4) ) Using โ๐ฆ=๐๐ฆ/๐๐ฅ โ๐ฅ โ๐ฆ=1/(4(๐ฅ)^( 3/4) ) โ๐ฅ Putting Values โ๐ฆ=1/(4(16)^( 3/4) ) . (โ1) โ๐ฆ=1/(4(2^4 )^( 3/4) ) (โ1) โ๐ฆ=(โ1)/(4 ร 2^3 ) โ๐ฆ=(โ1)/(4 ร 8) โ๐ฆ=(โ1)/32 โ๐ฆ=โ0. 03125 We know that โ๐ฆ=๐(๐ฅ+โ๐ฅ)โ๐(๐ฅ) โ๐ฆ=(๐ฅ+โ๐ฅ)^(1/4)โ(๐ฅ)^(1/4) Putting Values โ0. 03125=(16+(โ1))^( 1/4)โใ(16) ใ^(1/4) โ0. 03125=(16โ1)^( 1/4)โ(2)^(4 ร 1/4) โ0. 03125=(15)^( 1/4)โ2 โ0. 03125+2=(15)^( 1/4) โ0. 03125+2=(15)^( 1/4) 1. 96875=(15)^( 1/4) Thus, Approximate Value of (15)^( 1/4) is ๐. ๐๐๐๐๐

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.