Calculus IV – PRACTICE FINAL Columbia University Department of Mathematics Harvard University - MATH 2413Practice Final (b) solutions ALL ANSWERS 100% CORRECT

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Columbia University Department of Mathematics Calculus IV – PRACTICE FINAL (b) Instructor: Mike Miller 12/17/2020 Name: No calculator is allowed. Please give exact answers, including ⇡ and p... as appropriate; do not write answers with decimals. Show your work; partial credit will be given as appropriate. Distribution of Points Question Points Score 1 20 2 20 3 20 4 15 5 10 6 15 7 20 8 15 9 15 10 20 11 10 12 20 Total: 200 1Calculus IV PRACTICE FINAL (b) 12/17/2020 Exam time and submission This exam is available between 12AM and 11:59PM EST on December 17. You will submit your exam on Courseworks as you would a homework assignment. Submissions will no longer be available at mignight, and no exceptions will be made to this. You should, therefore, plan to start submitting plenty of time in advance of midnight, so that you can contact me if there are any unexpected technical issues. I suggest that you stop working by 11PM and start submitting then. Honor code This is an open book, open note exam; the book and the notes on Courseworks are the only authorized material for this exam. In particular, you may not refer to posted homework or practice midterm solutions; you may not use a calculator; you may not use other online references or tools; you may not communicate about the problems with other students. Any violation of this policy will be pursued as academic misconduct, as will any failure to report academic misconduct. You must sign and submit the following statement1 when submitting your exam. (If you don’t have a printer, copy the statement onto a piece of paper, sign below it, and submit that.) I a!rm that I have not plagiarized nor used unauthorized materials in taking this exam, nor have I given or received illegitimate help with this exam. Signature: 1This statement is modeled on the Columbia College code of honor. Page 2 of 15Calculus IV PRACTICE FINAL (b) 12/17/2020 1. (20 points) Compute the triple integral Z!31 Z0 2 Z!62 xyz dx dz dy. [Show More]

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