Calculus > QUESTIONS & ANSWERS > Harvard University - MATH 2413Practice Midterm 2(a) solutions. Columbia University Department of Ma (All)

Harvard University - MATH 2413Practice Midterm 2(a) solutions. Columbia University Department of Mathematics Calculus IV – MIDTERM #1. All Solutions Worked Out.

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Columbia University Department of Mathematics Calculus IV – MIDTERM #1 Instructor: Mike Miller 11/15/2020 Name: No calculator is allowed. Please give exact answers, including ⇡ and p as appr ... opriate; do not write answers with decimals. Show your work; partial credit will be given as appropriate. Distribution of Points Question Points Score Exam time and submission This exam is available between 9AM and 9PM EST on November 15. You will submit your exam on Courseworks as you would a homework assignment. Submissions will no longer be available after 9PM, and no exceptions will be made to this. You should, therefore, plan to start submitting plenty of time in advance of 9PM, so that you can contact me if there are any unexpected technical issues. I suggest that you stop working by 8PM 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 9 1. (15 points) Let C be the top half of the unit circle (oriented counterclockwise), 2. (15 points) Let C again be the top half of the unit circle oriented counterclockwise, but now let F = he!xy % xye!xy, %x2e!xyi and compute the line integral 5. Let S be the portion of the paraboloid x = 1%y2%z2 with %3  x  0, oriented in the negative x direction (the direction the paraboloid opens up in). (a) (5 points) Parameterize S. Is your parameterization oriented? 6. (15 points) Let C be a wobbly circle, parameterized by ~r(t) = (cos t, sin t, cos(8t) + 2) with 0  t  2⇡; this traces out a curve lying above the unit circle in the xy-plane, but whose height moves up and down as you traverse the curve. . [Show More]

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