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

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

Transcript

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 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.