Question 9 - Examples - Chapter 6 Class 12 Application of Derivatives
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Question 9 Use differential to approximate 〖(25)〗^(1/3)Let 𝑦 =𝑥^(1/3) Where 𝑥=27 and △𝑥=−2 Since 𝒚 =𝒙^(𝟏/𝟑) 𝑑𝑦/𝑑𝑥=𝑑(𝑥^(1/3) )/𝑑𝑥 = 1/3 𝑥^(1/3 − 1) = 1/3 𝑥^((−2)/3) 𝑑𝑦/𝑑𝑥=1/(3𝑥^(2/3) ) Now, ∆𝒚=𝒅𝒚/𝒅𝒙 ∆𝒙 ∆𝑦= 1/(3𝑥^(2/3) ) ∆𝑥 Putting values ∆𝑦= 1/(3(27)^(2/3) ) (−2) ∆𝑦= (−2)/(3 ×(3^3 )^(2/3) ) ∆𝑦= (−2)/(3 × 3^2 ) ∆𝑦= (−2)/27 ∆𝒚=−𝟎.𝟎𝟕𝟒 Now, (𝟐𝟓)^(𝟏/𝟑) =𝒚+∆𝒚 Putting values (25)^(1/3)=(27)^(1/3)−0.074 (25)^(1/3)=(3^3 )^(1/3)−0.074 (25)^(1/3)=3−0.074 (𝟐𝟓)^(𝟏/𝟑)=𝟐.𝟗𝟐𝟔 Hence, approximate value of (25)^(1/3) is 𝟐.𝟗𝟐𝟔
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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo