Math 215Homework Set 3:§§14.2 – 15.4Winter 2008Most of the following problems are modified versions of homework problems from your text bookMultivariable Calculusby James Stewart.14.2a. Sketch the curve described by the parametric equationr(t) =3 +etsin(t), etcos(t), et. Find anequation 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’sMultivariable Calculus. (Hint: Consider the functionf(t) =|r(t)|2.)15.1a. Problem 30 of§15.1 of Stewart’sMultivariable Calculus.15.1b. Problems 55–60 of§15.1 of Stewart’sMultivariable Calculus.15.1c. Describe the level surfaces of the functionf(x, y, z) =z2+x2-2y2.15.1d. Sketch the graph of the functionf(x, y) = 7-3x-4y.15.1e. Sketch the graph of the functionf(x, y) =16-16x2-y215.1f. Draw the circle of radius two centered at(1,1,1)and lying on the planex+y+z= 3. (Hint: Findtwo orthogonal unit vectors which are parallel to the plane. Use MAPLE to graph.)15.1g. Sketch the graph of the functionf(x, y) = 2x+ 3y. Sketch the graph described by the equation
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