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Unformatted text preview: Math 215 Homework Set 3: 13.7 15.1 Fall 2007 Most of the following problems are modified versions of the recommended homework problems from your text book Multivariable Calculus by James Stewart. 13.7b. Sketch the solid or surface described by the following equations and inequalities. (b) z - r2 = 0 (a) 0 /3, 5 (c) -/3 , 0 sec(), 0 /2 (e) r2 z 2 - r2 (f) 2 - 5 = -6 (d) 4 - sin = 0 (g) /4 3/4, z r 5 (h) = /3. 14.1a. Problems 19-24 of 14.1 of Stewart's Multivariable Calculus. 14.1b. Find parametric equations which describe the curve defined by intersecting the cylinder r = 7 with the paraboloid of revolution 7z + (x2 + y 2 ) = 0. Sketch the two surfaces and the curve of intersection. 14.2a. Sketch the curve described by the parametric equation r(t) = et sin(t), et cos(t), et . Find an equation which describes the tangent line to the curve at the point (0, 1, 1). Sketch the tangent line. 14.2b. Problem 50 of 14.2 of Stewart's Multivariable Calculus. (Hint: Consider the function f (t) = |r(t)|2 .) 15.1a. Problem 30 of 15.1 of Stewart's Multivariable Calculus. 15.1b. Problems 5560 of 15.1 of Stewart's Multivariable Calculus. 15.1c. Describe the level surfaces of the function f (x, y, z) = z 2 + x2 - y 2 . 15.1d. Sketch the graph of the function f (x, y) = 7 - 4x - 3y. 15.1e. Sketch the graph of the function f (x, y) = 9 - x2 - 9y 2 15.1f. Draw the circle of radius two centered at (1, 1, 1) and lying on the plane x + y + z = 3. (Hint: Find two orthogonal unit vectors which are parallel to the plane. Use MAPLE to graph.) 15.1g. Sketch the graph of the function f (x, y) = 2x + 3y. Sketch the graph described by the equation r - |z| = 0. Sketch the graph of the intersection of these two surfaces. (HINT: Use MAPLE.) ...
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This homework help was uploaded on 04/02/2008 for the course MATH 215 taught by Professor Fish during the Fall '08 term at University of Michigan.
- Fall '08
- Multivariable Calculus