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FINAL REVIEW #3-problems

# FINAL REVIEW #3-problems - suleimenov(bs26835 FINAL...

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suleimenov (bs26835) – FINAL REVIEW #3 – rusin – (55565) 1 This print-out should have 32 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. Third and final installment of the review for the final exam. Some questions may duplicate previous HW questions. These reviews have been very long and even so, are not exactly ”comprehensive” – there are many variations of the ideas that are not on these reviews. But I think if you are com- fortable with all the topics on these reviews, you will be in good shape for the exam. Good luck! 001 10.0points Find a vector function that represents the curve of intersection of the paraboloid z = x 2 + 3 y 2 and the parabolic cylinder y = x 2 . 1. r ( t ) = t i + t j + ( 3 t 2 + t 4 ) k 2. r ( t ) = t i + t j + ( t 2 + 3 t 4 ) k 3. r ( t ) = t 2 i + t j + ( t + 3 t 2 ) k 4. r ( t ) = t i + t 2 j + ( 3 t 2 + t 4 ) k 5. r ( t ) = t i + t 2 j + ( t 2 + 3 t 4 ) k 6. r ( t ) = t i + t j + ( t + 3 t 2 ) k 7. r ( t ) = t i + t j + ( 3 t + t 2 ) k 8. r ( t ) = t 2 i + t j + ( 3 t + t 2 ) k 002 10.0points Find an equation in vector form for the tangent line to the graph of r ( s ) = ( cos s, 2 e 3 s , sin s + 2 e - 3 s ) at the point (1 , 2 , 2). 1. L ( t ) = ( 1 , 2 2 t, 2 + 5 t ) 2. L ( t ) = ( t, 2 3 t, 2 5 t ) 3. L ( t ) = ( t, 2 2 t, 2 + 6 t ) 4. L ( t ) = ( 1 , 2 + 6 t, 2 6 t ) 5. L ( t ) = ( t, 2 + 3 t, 2 6 t ) 6. L ( t ) = ( 1 , 2 + 6 t, 2 5 t ) 003 10.0points Find the point of intersection of the tangent lines to the curve r ( t ) = ( sin πt, 4 sin πt, cos πt ) at the points where t = 0 and t = 0 . 5. 1. (1 , 4 , 1) 2. (0 , 0 , 0) 3. (1 , 4 , 1) 4. (1 , 3 , 0) 5. (0 , 4 , 1) 004 10.0points The curves given parametrically by x ( t ) = t, y ( t ) = t 6 , z ( t ) = t 3 , and x ( t ) = sin t, y ( t ) = sin 4 t, z ( t ) = t intersect at the origin. Find the cosine of their angle, θ , of inter- section. 1. cos θ = 2 3 2

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suleimenov (bs26835) – FINAL REVIEW #3 – rusin – (55565) 2 2. cos θ = 2 17 3. cos θ = 2 19 4. cos θ = 1 17 5. cos θ = 1 3 2 6. cos θ = 1 19 005 10.0points Find the unit vector T ( t ) tangent to the graph of the vector function r ( t ) = (big 2 t 2 , 4 t, 2 ln t )big . 1. T ( t ) = (Big t 2 2 t 2 + 1 , t 2 t 2 + 1 , 1 2 t 2 + 1 )Big 2. T ( t ) = (Big 2 t 2 t 2 + 1 , t t 2 + 1 , 1 t 2 + 1 )Big 3. T ( t ) = (Big t 2 2 t 2 + 1 , 2 t 2 t 2 + 1 , 1 2 t 2 + 1 )Big 4. T ( t ) = (Big 2 t 2 t 2 + 1 , 2 t t 2 + 1 , 1 t 2 + 1 )Big 5. T ( t ) = (Big 2 t 2 2 t 2 + 1 , 2 t 2 t 2 + 1 , 1 2 t 2 + 1 )Big 6. T ( t ) = (Big t 2 t 2 + 1 , t t 2 + 1 , 1 t 2 + 1 )Big 006 10.0points Determine the position vector, r (1), at time t = 1 for a particle moving in 3-space and having acceleration a ( t ) = 6 k when its initial velocity and position are given by v (0) = i + j 2 k , r (0) = 5 i + 2 j respectively.
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FINAL REVIEW #3-problems - suleimenov(bs26835 FINAL...

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