MAC 2313 Midterm: MAC 2313 FIU Exam 217fk
15 Feb 2019
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Prof. s. hudson: state the de nition of f (x, y) is di erentiable at p (x0, y0), show that the graph of r(t) = sin(t)i + 2 cos(t)j + 3 sin(t)k is a circle. If so, nd its value. lim (x,y) (0,0) xy2. 3x2 + 2y2: [10 pts] let f (x, y) = 2xy2, p (1, 2) and q(0. 99, 2. 02). At what rate is z changing with respect to x when the point is at (4, 3, 2) : [20 pts] answer t or f. you do not have to justify your answers: If fx and fy exist at p , then f (x, y) is di erentiable at p . If fx and fy exist at p , then f (x, y) is continuous at p . If the line x = 3 is a contour of f (x, y) through (3, 5) then fy(3, 5) = 0.
