Last updated at April 19, 2021 by Teachoo

Transcript

Example 22 Use differential to approximate ใ(25)ใ^(1/3)Let ๐ฆ =๐ฅ^(1/3) Where ๐ฅ=27 and โณ๐ฅ=โ2 Since ๐ =๐^(๐/๐) ๐๐ฆ/๐๐ฅ=๐(๐ฅ^(1/3) )/๐๐ฅ = 1/3 ๐ฅ^(1/3 โ 1) = 1/3 ๐ฅ^((โ2)/3) ๐๐ฆ/๐๐ฅ=1/(3๐ฅ^(2/3) ) Now, โ๐=๐ ๐/๐ ๐ โ๐ โ๐ฆ= 1/(3๐ฅ^(2/3) ) โ๐ฅ Putting values โ๐ฆ= 1/(3(27)^(2/3) ) (โ2) โ๐ฆ= (โ2)/(3 ร(3^3 )^(2/3) ) โ๐ฆ= (โ2)/(3 ร 3^2 ) โ๐ฆ= (โ2)/27 โ๐=โ๐.๐๐๐ Now, (๐๐)^(๐/๐) =๐+โ๐ Putting values (25)^(1/3)=(27)^(1/3)โ0.074 (25)^(1/3)=(3^3 )^(1/3)โ0.074 (25)^(1/3)=3โ0.074 (๐๐)^(๐/๐)=๐.๐๐๐ Hence, approximate value of (25)^(1/3) is ๐.๐๐๐

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About the Author

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.