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

Last updated at Dec. 16, 2024 by

Ex 6.4, 1 (ii) - Using differentials, find approximate value of √49.5

Ex 6.4, 1 (ii) - Chapter 6 Class 12 Application of Derivatives - Part 2
Ex 6.4, 1 (ii) - 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. (ii) √49.5Let y = √𝑥 where x = 49 & △ x = 0.5 Since y = √𝑥 𝑑𝑦/𝑑𝑥 = (𝑑(√𝑥))/𝑑𝑥 = 1/(2√𝑥) Now, ∆𝑦 = 𝑑𝑦/𝑑𝑥 △x = 1/(2√𝑥) (0.5) = 1/(2 × √49) × 0.5 = 1/(2 × 7) × 0.5 = 0.5/14 = 0.036 Also, ∆𝑦=𝑓(𝑥+∆𝑥)−𝑓(𝑥) Putting values ∆𝑦=√(𝑥+∆𝑥)−√𝑥 0. 036=√(49+0. 5)−√49 0. 036=√49.5−7 0. 036+7=√49.5 √49.5=7. 036 Hence, approximate value of √49.5 is 7.036

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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