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Unformatted text preview: Math 32A: Practice Problems for Exam 2 Problem 1. A particle travels along a path r ( t ) with acceleration vector ( t 4 , 4 − t ) . Find r ( t ) if at t = 0, the particle is located at the origin and has initial velocity v = ( 2 , 3 ) . Problem 2. Calculate f xy and f zxzw where f ( x, y, z, w ) = x 2 + ze w y sin( w 2 + w − 1 ) Problem 3. r ( s ) be a vector-valued function. What condition must be satisfied in order that r ( s ) be an arc length parametrization? Problem 4. Define the curvature of a path. Problem 5. A particle moves along the spiral path described by r ( t ) = t ( cos t, sin t ) The acceleration vector decomposes as a sum of tangential and normal acceleration: a ( t ) = a tan ( t ) + a nor ( t ) Calculate the a tan ( t ). Problem 6. Determine whether the following limits exist (give full explanation). lim ( x,y ) → x radicalbig x 2 + y 2 , lim ( x,y ) → xy radicalbig x 2 + y 2 Problem 7. At time t = t , the speed of a particle is 3 m/s and its tangent vector points along the positive...
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- Spring '08
- Math, lim, Arc length parametrization