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. (vi) ใ(15)ใ^(1/4)Let ๐ฆ=ใ๐ฅ ใ^(1/4) where ๐ฅ=16 , โ๐ฅ=โ1 Now, ๐ฆ=๐ฅ^( 1/4) Differentiating w.r.t.๐ฅ ๐๐ฆ/๐๐ฅ=๐(๐ฅ^( 1/4) )/๐๐ฅ=1/4 ๐ฅ^( (1 โ 4)/4 )=1/4 ๐ฅ^( (โ3)/( 4) ) Let ๐ฆ=ใ๐ฅ ใ^(1/4) where ๐ฅ=16 , โ๐ฅ=โ1 Now, ๐ฆ=๐ฅ^( 1/4) Differentiating w.r.t.๐ฅ ๐๐ฆ/๐๐ฅ=๐(๐ฅ^( 1/4) )/๐๐ฅ=1/4 ๐ฅ^( (1 โ 4)/4 )=1/4 ๐ฅ^( (โ3)/( 4) ) Using โ๐ฆ=๐๐ฆ/๐๐ฅ โ๐ฅ โ๐ฆ=1/(4(๐ฅ)^( 3/4) ) โ๐ฅ Putting Values โ๐ฆ=1/(4(16)^( 3/4) ) . (โ1) โ๐ฆ=1/(4(2^4 )^( 3/4) ) (โ1) โ๐ฆ=(โ1)/(4 ร 2^3 ) โ๐ฆ=(โ1)/(4 ร 8) โ๐ฆ=(โ1)/32 โ๐ฆ=โ0. 03125 We know that โ๐ฆ=๐(๐ฅ+โ๐ฅ)โ๐(๐ฅ) โ๐ฆ=(๐ฅ+โ๐ฅ)^(1/4)โ(๐ฅ)^(1/4) Putting Values โ0. 03125=(16+(โ1))^( 1/4)โใ(16) ใ^(1/4) โ0. 03125=(16โ1)^( 1/4)โ(2)^(4 ร 1/4) โ0. 03125=(15)^( 1/4)โ2 โ0. 03125+2=(15)^( 1/4) โ0. 03125+2=(15)^( 1/4) 1. 96875=(15)^( 1/4) Thus, Approximate Value of (15)^( 1/4) is ๐. ๐๐๐๐๐
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 You are here
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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