MATH 272 Final: MATH 272 Amherst S14M272 2802 Ndangali 29Final

• School: Amherst College
• Department: Mathematics and Statistics
• Course: MATH 272
• Professor: All

Document Summary

Read this first: this is a closed-book examination. No books, notes, calculators, cell phones, communication devices of any sort, or other aids are permitted: you need not simplify algebraically complicated answers. , arctan(cid:0) 3(cid:1), 43/2, eln 4, ln e7, e ln 5, e3 ln 3, or cosh (ln 3) should be simpli ed: please read each question carefully. Show all of your work and justify all of your answers. (you may use the backs of pages for additional work space. ) Find the angle between u = h2, 3, 1i and v = h4, 1, 2i. Convert the following integral from rectangular to cylindrical coordinates. Find the volume of the parallelepiped determined by u = h2, 2, 4i, v = h 2, 0, 2i, and w = h4, 3, 4i. Find the equation of the plane tangent to the surface z = ln (2x + y) at the point ( 1, 3).