Unformatted text preview: x = 1 ± y 2 and x = y 2 + z 2 (c) The intersection of the plane x + z = 1 and the ellipsoid x 2 + 4 y 2 + 4 z 2 = 1 Problem 3. Section 14.2 Find the equation of the tangent line to each of the following curves at the given point. (a) Curve: r 1 ( t ) = ± e t ;e 2 t ;e 3 t ² ; Point: r 1 (1) (b) Curve: r 2 ( t ) = ± e 2 t ± 4 ; sin( ± 4 t ) ;t 2 ² ; Point: (1 ; 1 ; 4) (c) Curve: r 3 ( t ) = r 1 ( t ) ² r 2 ( t + 1); Point: r 3 (1) Problem 4. Section 14.2 Let r ( t ) be a di±erentiable curve in R 3 which does not pass through the origin. (a) Show that d dt j r ( t ) j = 1 j r ( t ) j r ( t ) ³ r ( t ). (b) Show that if r ( t ) is perpendicular to r ( t ) for every t then the curve lies on the sphere x 2 + y 2 + z 2 = 1. Problem 5. Challenge Problem (will not be graded): Classify the curve x 2 + 4 xy + y 2 = 0 . 1...
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 '08
 WEINERMICHAELDA

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