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Misc 1 - Using differentials, find approximate value: 17/81

Misc 1 - Chapter 6 Class 12 Application of Derivatives - Part 2
Misc 1 - Chapter 6 Class 12 Application of Derivatives - Part 3 Misc 1 - Chapter 6 Class 12 Application of Derivatives - Part 4

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Misc 1 Using differentials, find the approximate value of each of the following: (a) (17/81)^(1/4) (17/81)^(1/4) = (17)^(1/4)/(81)^(1/4) = (17)^(1/4)/3 Let ๐‘ฆ =๐‘ฅ^(1/4) Where ๐‘ฅ=16 and โ–ณ๐‘ฅ=1 Since ๐’š =๐’™^(๐Ÿ/๐Ÿ’) ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=๐‘‘(๐‘ฅ^(1/4) )/๐‘‘๐‘ฅ = 1/4 ๐‘ฅ^(1/4 โˆ’ 1) = 1/4 ๐‘ฅ^((โˆ’3)/4) = 1/(4๐‘ฅ^(3/4) ) Now, โˆ†๐’š=๐’…๐’š/๐’…๐’™ โˆ†๐’™ โˆ†๐‘ฆ = (1/(4๐‘ฅ^(3/4) ))โˆ†๐‘ฅ Putting values โˆ†๐‘ฆ = 1/4 ร— 1/(16)^(3/4) ร— 1 = 1/4 ร— 1/(2^4 )^(3/4) = 1/4 ร— 1/2^3 = ๐Ÿ/๐Ÿ‘๐Ÿ Now, (17)^(1/4)=๐‘ฆ+โˆ†๐‘ฆ Putting values (17)^(1/4) = (16)^(1/4)+โˆ†๐‘ฆ (17)^(1/4) = (2^4 )^(1/4)+โˆ†๐‘ฆ (17)^(1/4) = 2+โˆ†๐‘ฆ (17)^(1/4) = 2 + 1/32 (17)^(1/4) = 2+ 0.03125 (๐Ÿ๐Ÿ•)^(๐Ÿ/๐Ÿ’) = 2.03125 Now, Approximate value of (๐Ÿ๐Ÿ•/๐Ÿ–๐Ÿ)^(๐Ÿ/๐Ÿ’) = (17)^(1/4)/3 = 2.03125/3 = 0.677 Hence, approximate value of (17/81)^(1/4) is 0.677 (As approximate value of (17)^(1/4) = 2.03125)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.