Example 22 - Use differential to approximate (25)1/3 - Examples

Example 22 - Chapter 6 Class 12 Application of Derivatives - Part 2
Example 22 - Chapter 6 Class 12 Application of Derivatives - Part 3

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

Transcript

Example 22 Use differential to approximate ใ€–(25)ใ€—^(1/3)Let ๐‘ฆ =๐‘ฅ^(1/3) Where ๐‘ฅ=27 and โ–ณ๐‘ฅ=โˆ’2 Since ๐’š =๐’™^(๐Ÿ/๐Ÿ‘) ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=๐‘‘(๐‘ฅ^(1/3) )/๐‘‘๐‘ฅ = 1/3 ๐‘ฅ^(1/3 โˆ’ 1) = 1/3 ๐‘ฅ^((โˆ’2)/3) ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=1/(3๐‘ฅ^(2/3) ) Now, โˆ†๐’š=๐’…๐’š/๐’…๐’™ โˆ†๐’™ โˆ†๐‘ฆ= 1/(3๐‘ฅ^(2/3) ) โˆ†๐‘ฅ Putting values โˆ†๐‘ฆ= 1/(3(27)^(2/3) ) (โˆ’2) โˆ†๐‘ฆ= (โˆ’2)/(3 ร—(3^3 )^(2/3) ) โˆ†๐‘ฆ= (โˆ’2)/(3 ร— 3^2 ) โˆ†๐‘ฆ= (โˆ’2)/27 โˆ†๐’š=โˆ’๐ŸŽ.๐ŸŽ๐Ÿ•๐Ÿ’ Now, (๐Ÿ๐Ÿ“)^(๐Ÿ/๐Ÿ‘) =๐’š+โˆ†๐’š Putting values (25)^(1/3)=(27)^(1/3)โˆ’0.074 (25)^(1/3)=(3^3 )^(1/3)โˆ’0.074 (25)^(1/3)=3โˆ’0.074 (๐Ÿ๐Ÿ“)^(๐Ÿ/๐Ÿ‘)=๐Ÿ.๐Ÿ—๐Ÿ๐Ÿ” Hence, approximate value of (25)^(1/3) is ๐Ÿ.๐Ÿ—๐Ÿ๐Ÿ”

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.