Check Full Chapter Explained - Continuity and Differentiability - Application of Derivatives (AOD) Class 12



Last updated at Aug. 18, 2020 by Teachoo
Check Full Chapter Explained - Continuity and Differentiability - Application of Derivatives (AOD) Class 12
Transcript
Ex 6.4, 1 Using differentials, find the approximate value of each of the following up to 3 places of decimal. (iv) ใ(0.009)ใ^(1/3) Let ๐ฆ=(๐ฅ)^(1/3) where ๐ฅ=0. 008 & โ๐ฅ=0. 001 Differentiating w.r.t.๐ฅ ๐๐ฆ/๐๐ฅ=๐(ใ๐ฅ ใ^(1/3) )/๐๐ฅ=1/3 ๐ฅ^((โ2)/3)=1/(3ใ ๐ฅใ^( 2/3) ) Using โ๐ฆ=๐๐ฆ/๐๐ฅ โ๐ฅ โ๐ฆ=1/(3ใ ๐ฅใ^( 2/3) ) รโ๐ฅ Putting Values โ๐ฆ=1/(3(0. 008)^( 2/3) ) ร0. 001 โ๐ฆ=(0. 001)/(3(8/1000)^(2/3) ) โ๐ฆ=(0. 001)/(3(2/10)^( 3 ร 2/3) ) โ๐ฆ=(0. 001)/(3(2/10)^2 ) โ๐ฆ=(0. 001)/(3 ร 4/100) โ๐ฆ=(0.001 ร 100)/12 โ๐ฆ=0. 008 We know that โ๐ฆ=๐(๐ฅ+โ๐ฅ)โ๐(๐ฅ) โ๐ฆ=ใ(๐ฅ+โ๐ฅ) ใ^(1/3)โใ๐ฅ ใ^(1/3) Putting Values 0. 008=(0. 008" " +0. 001)^( 1/3)โ(0. 008" " )^( 1/3) 0. 008=(0. 009)^( 1/3)โ(0. 008)^( 1/3) 0. 008=(0. 009)^( 1/3)โ(8/1000)^( 1/3) 0. 008=(0. 009)^( 1/3)โ(2/10)^( 3 ร 1/3) 0. 008=(0. 009)^( 1/3)โ(2/10) 0. 008=(0. 009)^( 1/3)โ0. 2 0. 008+0. 2=(0. 009)^( 1/3) (0. 009)^( 1/3)=0. 208 Thus , Approximate Value of (0 . 009)^(1/3) is ๐. ๐๐๐
Ex 6.4
Ex 6.4, 1 (ii) Not in Syllabus - CBSE Exams 2021
Ex 6.4, 1 (iii) Not in Syllabus - CBSE Exams 2021
Ex 6.4, 1 (iv) Not in Syllabus - CBSE Exams 2021 You are here
Ex 6.4, 1 (v) Not in Syllabus - CBSE Exams 2021
Ex 6.4, 1 (vi) Not in Syllabus - CBSE Exams 2021
Ex 6.4, 1 (vii) Not in Syllabus - CBSE Exams 2021
Ex 6.4, 1 (viii) Not in Syllabus - CBSE Exams 2021
Ex 6.4, 1 (ix) Not in Syllabus - CBSE Exams 2021
Ex 6.4, 1 (x) Not in Syllabus - CBSE Exams 2021
Ex 6.4, 1 (xi) Not in Syllabus - CBSE Exams 2021
Ex 6.4, 1 (xii) Not in Syllabus - CBSE Exams 2021
Ex 6.4, 1 (xiii) Not in Syllabus - CBSE Exams 2021
Ex 6.4, 1 (xiv) Not in Syllabus - CBSE Exams 2021
Ex 6.4, 1 (xv) Not in Syllabus - CBSE Exams 2021
Ex 6.4,2 Not in Syllabus - CBSE Exams 2021
Ex 6.4,3 Important Not in Syllabus - CBSE Exams 2021
Ex 6.4,4 Not in Syllabus - CBSE Exams 2021
Ex 6.4,5 Important Not in Syllabus - CBSE Exams 2021
Ex 6.4,6 Not in Syllabus - CBSE Exams 2021
Ex 6.4,7 Not in Syllabus - CBSE Exams 2021
Ex 6.4,8 Not in Syllabus - CBSE Exams 2021
Ex 6.4,9 Not in Syllabus - CBSE Exams 2021
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