Solution to Midterm 1.pdf - 2 MATH 202 SPRING 2015 INCLASS TEST 1(10 points part(a Find the orthogonal projection of vector ii =(1 2 3 on vector(7 =(3 0

# Solution to Midterm 1.pdf - 2 MATH 202 SPRING 2015 INCLASS...

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Unformatted text preview: 2 MATH 202, SPRING, 2015, IN—CLASS TEST 1. (10 points / part) (a) Find the orthogonal projection of vector ii = (1, 2, 3) on vector (7 = (3, 0, 4) 2:: U rogmiiwigiwwﬁm { g t w (c) Find the distance from the point (3, 2, 1) to the plane 2:1: — y —- z + 5 = 0. 9er MATH 202, SPRING, 2015, iN—CLASS TEST 3 2. Compute the following limits if they exist, otherwise, give the proof to show Why limits do not exist. (10 points/part) 1- 2 2 2 2 (a) (ac,y)1—E%O,0)(x +y )ln(x +y) (b) lim jig—2' (x,y,z)—&gt;(o,o,0) 9‘ +1, +2 4 MATH 202, SPRING, 2015, IN—CLASS TEST 3. A funtion f(a:, y,z) has continuous partial derivatives and satisﬁes f(0,1,=2) 3, “£03169: 1,2): 4, §1(0,1,2) = 3, 35012) :2 (5 points/part) (a) Find the directional derivative of f at (0, 1, 2) in the direction of the vector 17 = (l, ——2, 2). We} gﬁgftmn} of the gg thighs?“ A Z?“ vel surface f(:1:, y, z) - 3 at the point (0,1,.2) ((1)1? 33% 5 (t) and 17(t) are differentiable vector—valued functions, and that 1706) and 17(t) are orthogonal for all t. Prove that 12&quot; (t) - 2705) = —12'(t) - 27’(t). (10 points) 6 MATH 202, SPRING, 2015, IN-CLASS TEST 5. The line in R3 is given by the function W) = (2,1,2) +t(1,2,3). Let P be the plane that contains the line 1 and the point (4,2,0). Find a normal vector 17:: to the plane. (10 points) MATH 202, SPRING, 2015, IN—CLASS TEST 7 6. The function 2 2 2(22, y) is implicitly determined by the equation V xyzexyz + \$2 + 6 = 0 . a . Find g and 3%. (10 pomts) ...
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