Question 1 (xiv) - Approximations (using Differentiation) - Chapter 6 Class 12 Application of Derivatives

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Ex 6.4, 1 (xiv) - Find approximate value of (3.968)^1/2 - Teachoo

Ex 6.4, 1 (xiv) - Chapter 6 Class 12 Application of Derivatives - Part 2
Ex 6.4, 1 (xiv) - Chapter 6 Class 12 Application of Derivatives - Part 3

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Question 1 Using differentials, find the approximate value of each of the following up to 3 places of decimal. (xiv) 〖(3.968)〗^(3/2)Let 𝑦=𝑥^( 3/2) where 𝑥=4 & ∆𝑥=−0. 032 Now, 𝑦=𝑥^( 3/2) Differentiating w.r.t.𝑥 𝑑𝑦/𝑑𝑥=𝑑(𝑥^( 3/2) )/𝑑𝑥 𝑑𝑦/𝑑𝑥=3/2 〖𝑥 〗^(1/2) Using ∆𝑦=𝑑𝑦/𝑑𝑥 ∆𝑥 ∆𝑦=3/2 𝑥^( 1/2) ∆𝑥 Putting Values ∆𝑦=3/2 (4)^( 1/2) . (−0. 032) ∆𝑦=3/2 (2^2 )^( 1/2) . (−0. 032) ∆𝑦=3/2 × 2 × (−0. 032) ∆𝑦=3 × (−0. 032) ∆𝑦=−0. 096 We know that ∆𝑦=𝑓(𝑥+∆𝑥)−𝑓(𝑥) So, ∆𝑦=(𝑥+∆𝑥)^( 3/2)−𝑥^( 3/2) Putting Values −0. 096=(4+(−0. 032))^( 3/2)−(4)^( 3/2) −0. 096=(4−0. 032)^( 3/2)−〖(2)^2〗^( × 3/2) −0. 096=(3. 968)^( 3/2)−2^3 −0. 096=(3. 968)^( 3/2)−8 −0. 096+8=(3. 968)^( 3/2) 7. 904=(3. 968)^( 3/2) (3. 968)^( 3/2)=7.904 Thus, Approximate Values of (3. 968)^( 3/2) is 𝟕. 𝟗𝟎𝟒

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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