1617-257/Homework Assignment 8 Solutions: Difference between revisions
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(Created page with "{{1617-257/Navigation}} ==Doing== '''Solve''' ''all'' the problems in sections 13-14, but submit only your solutions of problem 4 in section 14 and problems 4 and 8 in sectio...") |
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==Doing== |
==Doing== |
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'''Solve''' ''all'' the problems in |
'''Solve''' ''all'' the problems in section 12, but submit only your solutions of problem 3. In addition, solve and submit your solution of the following problem: |
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<u>'''Problem A.'''</u> Let <math>Q=[0,1]^3</math> and let <math>f\colon Q\to{\mathbb R}</math> be given by <math>f(x,y,z)=1</math> if <math>x<y<z</math>, and <math>f(x,y,z)=0</math> otherwise. Compute <math>\int_Qf</math>. (This problem is merely about computations. You may assume without proof that <math>f</math> and all other functions you may encounter along the computation are integrable). |
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<u>'''Problem A.'''</u> Compute the volume of the "2D ice cream cone", <math>C=\left\{(x,y)\colon |x|\leq y\leq 1+\sqrt{1-x^2}\right\}</math>. |
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<u>'''Problem B.'''</u> Compute the volume of the "n-dimensional simplex" <math>\Delta_n=\left\{(t_1,\ldots,t_n)\colon 0\leq t_1\leq t_2\leq\ldots\leq t_n\leq 1\right\}</math>. |
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[[Media:1617-257_HW8_assignment.pdf|HW8 pdf]] |
[[Media:1617-257_HW8_assignment.pdf|HW8 pdf]] |
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Revision as of 17:02, 25 November 2016
Doing
Solve all the problems in section 12, but submit only your solutions of problem 3. In addition, solve and submit your solution of the following problem:
Problem A. Let and let be given by if , and otherwise. Compute . (This problem is merely about computations. You may assume without proof that and all other functions you may encounter along the computation are integrable).
![{\displaystyle Q=[0,1]^{3}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/185a3872cd502e733135b57f23d0d45eed50ceb6)
