LueckePracticeExam1

LueckePracticeExam1 - y 2 + 40 y + 4 x 2-20 = 0. 8. Find...

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Name and EID: M 408M Exam 1 Luecke 10/3/07 In the problems below indicate your answers by drawing boxes around them. You must show your work to get credit for a problem. 1. Find the length from t = 0 to t = 1 of the parametric curve x = 5 - t 2 ,y = 1 + 2 t 3 .
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2. Sketch the graph of one loop of the polar curve r = 3 sin(2 θ ). 3. Compute the area of one loop of r = 3 sin(2 θ ) (graphed above).
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4. Let L be the line through the points P(1,0,-2) and Q(-1,4,2). Find two direction vectors for L with length 3. 5. Find the symmetric equations for the line L through the points P(1,0,-2) and Q(- 1,4,2). Note that this line is the same as for Problem 4.
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6. Find an equation of the plane through the point (1 , - 2 , 0) that is parallel to the plane 2 x - 4 y + 7 z - 4 = 0. 7. Find the vertex or vertices of 5
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Unformatted text preview: y 2 + 40 y + 4 x 2-20 = 0. 8. Find the slope of the tangent line to the polar curve r = 1 + 4 sin( θ ) when θ = π/ 4. 9. Compute the cosine of the angle between a = < 1 ,-2 , 3 > and b = < 2 , ,-1 > . Assume the paper is the plane containing these vectors and we are looking down on these vectors as pictured to the right. Would a × b be pointing into or out of the page? 10. Find the equation of the plane containing the points P (1 , , 0), Q (0 ,-3 , 0), R (0 , ,-5). 11. Graph the cross-section (trace) in the plane y = 3 of the surface in R 3 given by z 2 25 + y 2-x 2 4 = 5 Label the axes of the plane....
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LueckePracticeExam1 - y 2 + 40 y + 4 x 2-20 = 0. 8. Find...

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