Question 8 - Finding approximate value of numbers - Chapter 6 Class 12 Application of Derivatives

Last updated at Dec. 16, 2024 by

Example 21 - Use differential to approximate root 36.6 - Examples

Example 21 - Chapter 6 Class 12 Application of Derivatives - Part 2

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Question 8 Use differential to approximate √36.6Let y = √𝑥 where x = 36 & △ x = 0.6 Since y = √𝒙 𝑑𝑦/𝑑𝑥 = (𝑑(√𝑥))/𝑑𝑥 = 1/(2√𝑥) Now, ∆𝑦 = 𝑑𝑦/𝑑𝑥 △x = 1/(2√𝑥) (0.6) = 0.6/(2 × √36) = 0.6/(2 × 6) = 0.05 Now, √36.6=𝑦+∆𝑦 Putting values √36.6=√36+0.05 √36.6=6+0.05 √(𝟑𝟔.𝟔) = 6.05 Hence, approximate value of √36.6 is 6.05

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