Exam 1 Practice

Exam 1 Practice - x-axis in the usual fashion. 25 (a)...

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Math 2414 Exam 1 Practice Spring 2011 1. (a) Find the standard equation of the sphere that contains the point P (5,-2,-1) and has center C (-1,0,-4). (b) The intersection of the sphere in part (a) and the xy plane is a curve. Find an equation of the curve of intersection. (c) Determine whether the graph of the following equation is a sphere, if so, identify its center and radius. Yes C (2,-5,1) and r = 2. 26 2 10 4 2 2 2 = + z z y y x x 2. Given vectors , k j i a 3 2 + = k i b + = 2 , k j c + = 5 (a) Find a vector with magnitude 5 in the same direction as c. (b) Find the direction cosines of a . (c) Determine whether any two of vectors a, b, or c are orthogonal . (d) Find the angle between a and b to the nearest degree . (e) Find a c proj 3. Suppose 500 1 = V and has direction and ° 70 60 2 = V and has direction where the angles are measured from the positive
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Unformatted text preview: x-axis in the usual fashion. 25 (a) Sketch vectors , , and the resultant 1 V 2 V 2 1 V V + in the plane. (b) Compute the magnitude and direction of the resultant vector 2 1 V V + . (c) Does the vector point into the page or out of it? 2 1 V V 4. Given vectors , k j i a 3 2 + = k i b + = 2 , k j c + = 5 (a) find c b (b) find a unit vector orthogonal to b and c. (c) Calculate a . In this instance, can the result of the scalar triple product be interpreted as the volume of a parallelepiped? ) ( c b 5. Evaluate the integral. dx e x x 2 3 cos 6. Evaluate the integral. 3 dx x x x 2 4 2 cos cos sin 7. Use trigonometric substitution to evaluate the integral dx x x 25 1 2 4 Page 1 of 1...
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