Example 21 - Use differential to approximate root 36.6 - Examples

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  1. Chapter 6 Class 12 Application of Derivatives
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Example 21 Use differential to approximate ﷐﷮36.6﷯ Let y = ﷐﷮𝑥﷯ Let 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) = ﷐1﷮2﷐﷮36﷯﷯ (0.6) = ﷐0.6﷮2 × 6﷯ = 0.05 Also, ∆𝑦=𝑓﷐𝑥+∆𝑥﷯−𝑓﷐𝑥﷯ Putting values 0.05=﷐﷮36+0.6﷯−﷐﷮36﷯ ﷐﷮36.6﷯=0.05+﷐﷮36﷯ ﷐﷮36.6﷯=0.05+6 ∆𝑦 = ﷐﷮𝑥+△x﷯ − ﷐﷮𝑥﷯ ﷐﷮36.6﷯ = 6.05 Hence, approximate value of ﷐﷮36.6﷯ is 6.05

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