Question 1 (a) - Miscellaneous - Chapter 6 Class 12 Application of Derivatives
Last updated at August 5, 2026 by Teachoo
Miscellaneous
Misc 1
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Chapter 6 Class 12 Application of Derivatives
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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 š¦ =š„^(1/4) Where š„=16 and ā³š„=1 Since š =š^(š/š) šš¦/šš„=š(š„^(1/4) )/šš„ = 1/4 š„^(1/4 ā 1) = 1/4 š„^((ā3)/4) = 1/(4š„^(3/4) ) Now, āš=š š/š š āš āš¦ = (1/(4š„^(3/4) ))āš„ Putting values āš¦ = 1/4 Ć 1/(16)^(3/4) Ć 1 = 1/4 Ć 1/(2^4 )^(3/4) = 1/4 Ć 1/2^3 = š/šš Now, (17)^(1/4)=š¦+āš¦ Putting values (17)^(1/4) = (16)^(1/4)+āš¦ (17)^(1/4) = (2^4 )^(1/4)+āš¦ (17)^(1/4) = 2+āš¦ (17)^(1/4) = 2 + 1/32 (17)^(1/4) = 2+ 0.03125 (šš)^(š/š) = 2.03125 Now, Approximate value of (šš/šš)^(š/š) = (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)
