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

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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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Question 8 Use differential to approximate โˆš36.6Let y = โˆš๐‘ฅ where x = 36 & โ–ณ x = 0.6 Since y = โˆš๐’™ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = (๐‘‘(โˆš๐‘ฅ))/๐‘‘๐‘ฅ = 1/(2โˆš๐‘ฅ) Now, โˆ†๐‘ฆ = ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ โ–ณx = 1/(2โˆš๐‘ฅ) (0.6) = 0.6/(2 ร— โˆš36) = 0.6/(2 ร— 6) = 0.05 Now, โˆš36.6=๐‘ฆ+โˆ†๐‘ฆ Putting values โˆš36.6=โˆš36+0.05 โˆš36.6=6+0.05 โˆš(๐Ÿ‘๐Ÿ”.๐Ÿ”) = 6.05 Hence, approximate value of โˆš36.6 is 6.05

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