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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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Example 21 Use differential to approximate √36.6Let y = √π‘₯ where x = 36 & β–³ x = 0.6 Since y = βˆšπ’™ 𝑑𝑦/𝑑π‘₯ = (𝑑(√π‘₯))/𝑑π‘₯ = 1/(2√π‘₯) Now, βˆ†π‘¦ = 𝑑𝑦/𝑑π‘₯ β–³x = 1/(2√π‘₯) (0.6) = 0.6/(2 Γ— √36) = 0.6/(2 Γ— 6) = 0.05 Now, √36.6=𝑦+βˆ†π‘¦ Putting values √36.6=√36+0.05 √36.6=6+0.05 √(πŸ‘πŸ”.πŸ”) = 6.05 Hence, approximate value of √36.6 is 6.05

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