1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise
  3. Approximations (using Differentiation)
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Question 1 (ii) - Approximations (using Differentiation) - Chapter 6 Class 12 Application of Derivatives

Last updated at Dec. 16, 2024 by Teachoo

Transcript

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
  1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise

    3. Approximations (using Differentiation)

    Finding rate of change →
Finding rate of change →
Chapter 6 Class 12 Application of Derivatives
Serial order wise

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Davneet Singh

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