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Chapter 6 Class 12 Application of Derivatives
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Question 9 - Examples - Chapter 6 Class 12 Application of Derivatives

Last updated at April 16, 2024 by

Example 22 - Use differential to approximate (25)1/3 - Examples

Example 22 - Chapter 6 Class 12 Application of Derivatives - Part 2
Example 22 - Chapter 6 Class 12 Application of Derivatives - Part 3

Transcript

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, Social Science, Physics, Chemistry, Computer Science at Teachoo.