1. Chapter 6 Class 12 Application of Derivatives (Term 1)
  2. Serial order wise
  3. Ex 6.4

Ex 6.4, 1 (ii) - Chapter 6 Class 12 Application of Derivatives (Term 1)

Last updated at April 15, 2021 by

Ex 6.4, 1 (ii) - Using differentials, find approximate value of √49.5

Ex 6.4, 1 (ii) - Chapter 6 Class 12 Application of Derivatives - Part 2
Ex 6.4, 1 (ii) - Chapter 6 Class 12 Application of Derivatives - Part 3

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

    3. Ex 6.4

    Ex 6.5 →

Transcript

Ex 6.4, 1 Using differentials, find the approximate value of each of the following up to 3 places of decimal. (ii) โˆš49.5Let y = โˆš๐‘ฅ where x = 49 & โ–ณ x = 0.5 Since y = โˆš๐‘ฅ 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) (0.5) = 1/(2 ร— โˆš49) ร— 0.5 = 1/(2 ร— 7) ร— 0.5 = 0.5/14 = 0.036 Also, โˆ†๐‘ฆ=๐‘“(๐‘ฅ+โˆ†๐‘ฅ)โˆ’๐‘“(๐‘ฅ) Putting values โˆ†๐‘ฆ=โˆš(๐‘ฅ+โˆ†๐‘ฅ)โˆ’โˆš๐‘ฅ 0. 036=โˆš(49+0. 5)โˆ’โˆš49 0. 036=โˆš49.5โˆ’7 0. 036+7=โˆš49.5 โˆš49.5=7. 036 Hence, approximate value of โˆš49.5 is 7.036

Chapter 6 Class 12 Application of Derivatives (Term 1)
Serial order wise

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