MATH 2263 Midterm: MATH 2263 UMN Exam 3 SolutionsSpring 08
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April 24, 2008: (10 points) let b be the rectangular solid 0 x 4, 1 y 2, 0 z 2. Solution: xz2 y2 = x y 2 z2, so rrrb. 3 . x=0 xz2 y2 dv = r 4. 0 z2 dz : (20 points) let ~f be the vector eld (a) (10 points) find a real-valued function f (x, y) so that. ~f (x, y) = (y2 + ex)~i + 2xy~j. Y implies that f (x, y) = xy2 + g(x) for some function g of one variable. Di erentiating this formula with respect to x yields f. X = y2 + g (x), so we need g (x) = ex and so g(x) = ex + c. X = y2 + ex and f f (x, y) = xy2 + ex + c. (b) (10 points) let c be the curve given by x = cos(t2 ) and y = t, 0 t 2.
