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. (xii) ใ(26.57)ใ^(1/3) Let ๐ฆ=๐ฅ^( 1/3) where ๐ฅ=27 & โ ๐ฅ=โ0. 43 Now, ๐ฆ=๐ฅ^( 1/3) Differentiating w.r.t.๐ฅ ๐๐ฆ/๐๐ฅ=๐(๐ฅ^( 1/3) )/๐๐ฅ=1/3 ๐ฅ^( 1/3 โ 1)=1/3 ๐ฅ^( (โ 2)/( 3))=1/(3 ๐ฅ^( 2/( 3)) ) Using โ๐ฆ=๐๐ฆ/๐๐ฅ โ๐ฅ โ๐ฆ=1/(3 ๐ฅ^( 2/( 3)) ) ร โ๐ฅ Putting Values โ๐ฆ=1/(3 (27)^( 2/( 3)) ) ร (โ0. 43) โ๐ฆ=(โ0. 43)/(3 ร 3^(3 ร 2/( 3)) ) โ๐ฆ=(โ0. 43)/(3 ร 3^2 ) โ๐ฆ=(โ0. 43)/(3 ร 9) โ๐ฆ=(โ0. 43)/27 โ๐ฆ=โ0. 015926 We know that โ๐ฆ=๐(๐ฅ+โ๐ฅ)โ๐(๐ฅ) So, โ๐ฆ=ใ(๐ฅ+โ๐ฅ) ใ^(1/3)โ๐ฅ^( 1/3) Putting Values โ0. 015926=(27+(โ0. 43))^( 1/3)โ(27)^( 1/3) โ0. 015926=(26. 57)^( 1/3)โ(27)^( 3 ร 1/3) โ0. 015926=(26. 57)^( 1/3)โ3 โ0. 015926+3=(26. 53)^( 1/3) 2. 984=(26. 53)^( 1/3) Thus, the Approximate Values of (26. 53)^( 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
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 You are here
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
About the Author