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hmwk3 - Math 215 Homework Set 3 14.2 15.4 Winter 2008 Most...

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Math 215 Homework Set 3: §§ 14.2 – 15.4 Winter 2008 Most of the following problems are modified versions of homework problems from your text book Multivariable Calculus by James Stewart. 14.2a. Sketch the curve described by the parametric equation r ( t ) = 3 + e t sin( t ) , e t cos( t ) , e t . 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 55–60 of § 15.1 of Stewart’s Multivariable Calculus . 15.1c. Describe the level surfaces of the function f ( x, y, z ) = z 2 + x 2 - 2 y 2 . 15.1d. Sketch the graph of the function f ( x, y ) = 7 - 3 x - 4 y . 15.1e. Sketch the graph of the function f ( x, y ) = 16 - 16 x 2 - y 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 ) = 2 x + 3 y . Sketch the graph described by the equation
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