MATH 2210 Midterm: Math2210-02-03_Fall2011
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Tuesday, december 13, 2011 (8:00 am - noon) Calculators and formula sheets are not allowed: show your work on the blank space beneath each question. Let a =< 2, 3, 6 > and b =< 5, 1, 4 >. (a) find the scalar projection of b onto a, compab. 2 (b) find the vector projection of b onto a, projab: (10 points) Given the function f (x, y) = x2 sin2 y x2+2y2 , (a) determine the set of points at which the function is continuous. Otherwise, show that the limit does not exist: (5 points) Find the linear approximation of the function f (x, y, z) = px2 + y2 + z2 at (3, 2, 6) and use it to approximate the number p(3. 02)2 + (1. 97)2 + (5. 99)2. Note: you do not need to calculate the nal result of the approximation forp(3. 02)2 + (1. 97)2 + (5. 99)2, i. e. , leave the approximation as a sum of fractions.
