MATH 431 Midterm: MATH431 HELZER-G SPRING2003 0101 MID EXAM 1

Find the center and the radius of the sphere whose equation is x2 + 2x + y2 - y + z2 = 0. Let A rightarrow =, B rightarrow = and C rightarrow =, find a value for z which guarantees that all the three vectors are coplanar. Let A rightarrow = and B rightarrow =. Find the value of c such that A rightarrow and B rightarrow are orthogonal. Find the value of c such that A rightarrow and B rightarrow are parallel. Determine whether the lines L1 : x = l + t,.y = 2 + 3t, z = 3 + t and L2 : x = l + t, y = 3 + 4t, z = 4 + 2t are parallel, intersecting, or skew. If they intersect, find the point of intersection. Let L be the line given by x = 3 - t, y = 2 + t, z = -4 + 2t. L intersects the plane 3x - 2y + z = 1 at the point P = (3,2,-4). Find parametric equations for the line through P which lies in the plane and is perpendicular to L. Find the coordinates of the point(s) of intersection of the line x = l + t, y = 2 + 3t, z = l - t and the surface z = x2 + 2y2.

the the par tere at time t = 3. (d particle eding justify . 、sponse. c) Find ding up, slowing down or neither at t = 3? ion of the particle at time t = 3. d th d) Find the 4. (c 2. (no calculat 4 2 Let F(x) =にf(ta. The graph off on the interval [-3,4] 1 consists of 2 line segments and a semicircle, as shown in the graph above. (a) Find F(0), F'(0), and F(4) (b) minimum values of F(x) on the interval Find all relative L-3,4]. Justify your answer. of (c) Find the e-coordinates of the inflection points of Flx) on the interval [-3, 4]. Justify your answe. x =te the equation of the line tangent to the point where 0 3 5 7 8 12 44 40 3. (ealculator) t (minutes)

Name: Math 273-03, Written Assignment 13 I prefer that you submit your answers on a printed copy of this document, like it's a quiz or exam. However you may instead rewrite the questions by hand before solving them. Staple sheets together, in order. Be neat. Always give enough work and clear explanation so that fellow students could follow what you did (from start to finish) just by reading your paper. Numbers in [] give point values for each question. Let the closed curve C consist of the line segment from (11) to (01), followed by the line segment from (0,1) to (0,0), followed by the piece of y-2 from (0,0) to (1,1). Also, let F-G, x2y〉 a) ] Graph C, indicating its orientation with an arrow. b) [8] Find φ F-T ds by integrating F over each piece of C and adding the results.