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  1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise

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 ๐‘ฆ=ใ€–๐‘ฅ ใ€—^(1/4) where ๐‘ฅ=16 , โˆ†๐‘ฅ=โˆ’1 Now, ๐‘ฆ=๐‘ฅ^( 1/4) Differentiating w.r.t.๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=๐‘‘(๐‘ฅ^( 1/4) )/๐‘‘๐‘ฅ=1/4 ๐‘ฅ^( (1 โˆ’ 4)/4 )=1/4 ๐‘ฅ^( (โˆ’3)/( 4) ) Let ๐‘ฆ=ใ€–๐‘ฅ ใ€—^(1/4) where ๐‘ฅ=16 , โˆ†๐‘ฅ=โˆ’1 Now, ๐‘ฆ=๐‘ฅ^( 1/4) Differentiating w.r.t.๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=๐‘‘(๐‘ฅ^( 1/4) )/๐‘‘๐‘ฅ=1/4 ๐‘ฅ^( (1 โˆ’ 4)/4 )=1/4 ๐‘ฅ^( (โˆ’3)/( 4) ) Using โˆ†๐‘ฆ=๐‘‘๐‘ฆ/๐‘‘๐‘ฅ โˆ†๐‘ฅ โˆ†๐‘ฆ=1/(4(๐‘ฅ)^( 3/4) ) โˆ†๐‘ฅ Putting Values โˆ†๐‘ฆ=1/(4(16)^( 3/4) ) . (โˆ’1) โˆ†๐‘ฆ=1/(4(2^4 )^( 3/4) ) (โˆ’1) โˆ†๐‘ฆ=(โˆ’1)/(4 ร— 2^3 ) โˆ†๐‘ฆ=(โˆ’1)/(4 ร— 8) โˆ†๐‘ฆ=(โˆ’1)/32 โˆ†๐‘ฆ=โˆ’0. 03125 We know that โˆ†๐‘ฆ=๐‘“(๐‘ฅ+โˆ†๐‘ฅ)โˆ’๐‘“(๐‘ฅ) โˆ†๐‘ฆ=(๐‘ฅ+โˆ†๐‘ฅ)^(1/4)โˆ’(๐‘ฅ)^(1/4) Putting Values โˆ’0. 03125=(16+(โˆ’1))^( 1/4)โˆ’ใ€–(16) ใ€—^(1/4) โˆ’0. 03125=(16โˆ’1)^( 1/4)โˆ’(2)^(4 ร— 1/4) โˆ’0. 03125=(15)^( 1/4)โˆ’2 โˆ’0. 03125+2=(15)^( 1/4) โˆ’0. 03125+2=(15)^( 1/4) 1. 96875=(15)^( 1/4) Thus, Approximate Value of (15)^( 1/4) is ๐Ÿ. ๐Ÿ—๐Ÿ”๐Ÿ–๐Ÿ•๐Ÿ“

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.