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

Last updated at Jan. 7, 2020 by Teachoo
Check Full Chapter Explained - Continuity and Differentiability - Application of Derivatives (AOD) Class 12
Transcript
Ex 6.1, 13 A balloon, which always remains spherical, has a variable diameter 3/2 (2๐ฅ +1). Find the rate of change of its volume with respect to ๐ฅ. Let d be the diameter of the balloon Given d = 3/2 (2x + 1) Let r be the radius of the balloon r = ๐/2 = 3/4 (2x + 1) The balloon is a sphere Volume of the balloon = Volume of sphere = 4/3 ๐๐^3 We need to find rate of change of volume with respect to x that is ๐๐ฃ/๐๐ฅ ๐๐ฃ/๐๐ฅ = ๐/๐๐ฅ (4/3 ๐๐^3 ) = 4๐/3 (๐๐^3)/๐๐ฅ = 4๐/3 ๐/๐๐ฅ (27/64 (2๐ฅ+1)^3 ) = 9๐/16 (๐(2๐ฅ + 1)^3)/๐๐ฅ = 9๐/16 3(2x + 1)2 (2) = ๐๐๐ /๐ (๐๐+๐)^๐ Hence, ๐๐ฃ/๐๐ฅ = 27๐/8 (2๐ฅ+1)^2
Ex 6.1
Ex 6.1,2 Not in Syllabus - CBSE Exams 2021
Ex 6.1,3 Not in Syllabus - CBSE Exams 2021
Ex 6.1,4 Important Not in Syllabus - CBSE Exams 2021
Ex 6.1,5 Important Not in Syllabus - CBSE Exams 2021
Ex 6.1,6 Not in Syllabus - CBSE Exams 2021
Ex 6.1,7 Not in Syllabus - CBSE Exams 2021
Ex 6.1,8 Not in Syllabus - CBSE Exams 2021
Ex 6.1,9 Not in Syllabus - CBSE Exams 2021
Ex 6.1,10 Important Not in Syllabus - CBSE Exams 2021
Ex 6.1,11 Important Not in Syllabus - CBSE Exams 2021
Ex 6.1,12 Not in Syllabus - CBSE Exams 2021
Ex 6.1,13 Important Not in Syllabus - CBSE Exams 2021 You are here
Ex 6.1,14 Not in Syllabus - CBSE Exams 2021
Ex 6.1,15 Important Not in Syllabus - CBSE Exams 2021
Ex 6.1,16 Not in Syllabus - CBSE Exams 2021
Ex 6.1,17 Not in Syllabus - CBSE Exams 2021
Ex 6.1, 18 Not in Syllabus - CBSE Exams 2021
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