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. (xv) ใ(32.15)ใ^(1/5) Let ๐ฆ=(๐ฅ)^( 1/5) where ๐ฅ=32 & โ๐ฅ=0. 15 Now, ๐ฆ=(๐ฅ)^( 1/5) Differentiating w.r.t.๐ฅ ๐๐ฆ/๐๐ฅ=๐(๐ฅ^( 1/5) )/๐๐ฅ=1/5 ๐ฅ^( 1/5 โ 1) =1/5 ๐ฅ^( (โ 4)/( 5) )=1/(5ใ ๐ฅใ^( 4/5 ) ) Using โ๐ฆ=๐๐ฆ/๐๐ฅ โ๐ฅ โ๐ฆ=1/(5 ใ๐ฅ ใ^(4/5) ) โ๐ฅ Putting Values โ๐ฆ=1/(5(32)^( 4/5) ) ร (0. 15) โ๐ฆ=1/(5(2)^( 5 ร 4/5) ) ร (0. 15) โ๐ฆ=1/(5(2)^( 4) ) ร (0. 15) โ๐ฆ=1/(5 ร 16) ร 0. 15 โ๐ฆ=(0. 15" " )/80 โ๐ฆ=0. 00187 We know that โ๐ฆ=๐(๐ฅ+โ๐ฅ)โ๐(๐ฅ) So, โ๐ฆ=(๐ฅ+โ๐ฅ)^( 1/5)โใ๐ฅ ใ^(1/5) Putting Values 0. 00187=(32+0. 15)^( 1/5)โ(32)^( 1/5) 0. 00187=(32. 15)^( 1/5)โ(2)^(5 ร 1/5 ) 0. 00187=(32. 15)^( 1/5)โ2 0. 00187+2=(32. 15)^( 1/5) 2. 00187=(32. 15)^( 1/5) (32. 15)^( 1/5)=2. 00187 Hence, Approximate Values of (32. 15)^( 1/5) 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
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 You are here
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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