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. (viii) ใ(255)ใ^(1/4) Let ๐ฆ=(๐ฅ)^(1/4) where ๐ฅ=256 & โ๐ฅ=โ1 Now, ๐ฆ=(๐ฅ)^(1/4) Differentiating w.r.t.๐ฅ ๐๐ฆ/๐๐ฅ=๐(ใ๐ฅ ใ^(1/4) )/๐๐ฅ=1/4 ๐ฅ^( 1/4 โ 1) =1/4 ๐ฅ^( (โ3)/( 4))=1/(4 ๐ฅ^( 3/( 4)) ) Using โ๐ฆ=๐๐ฆ/๐๐ฅ โ๐ฅ โ๐ฆ=1/(4ใ ๐ฅใ^( 3/( 4)) ) รโ๐ฅ Putting Values โ๐ฆ=1/(4 (256)^(3/4) ) ร (โ1) โ๐ฆ=(โ 1)/(4 (4^4 )^(3/4) ) โ๐ฆ=(โ 1)/(4 ร 4^3 ) โ๐ฆ=(โ 1)/(4 ร 64) โ๐ฆ=(โ 1)/256 โ๐ฆ=โ0. 0039 We know that โ๐ฆ=๐(๐ฅ+โ๐ฅ)โ๐(๐ฅ) โ๐ฆ=ใ(๐ฅ+โ๐ฅ) ใ^(1/4)โ๐ฅ^( 1/4) Putting Values โ0. 0039=ใ(256+(โ1)) ใ^(1/4)โ(256)^( 1/4) โ0. 0039=ใ(255) ใ^(1/4)โ(4^4 )^( 1/4) โ0. 0039=ใ(255) ใ^(1/4)โ4 โ0. 0039=ใ(255) ใ^(1/4)โ4 โ0. 0039+4=ใ(255) ใ^(1/4) 3. 9961=ใ(255) ใ^(1/4) Thus, the Approximate Values of ใ(255) ใ^(1/4) is ๐. ๐๐๐๐
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 You are here
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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