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WSU.S2010.M273.InClassFinalExamReview

WSU.S2010.M273.InClassFinalExamReview - Final Exam Review...

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Final Exam Review Problems 1. Section 10.8 Arc Length : Find the length of the curve r ( t ) = i + t 2 j + t 3 k , where 0 t 1. 2. Section 11.5 Chain Rule : Find u p , u r , u ∂θ , given u = x 2 + yz , x = pr cos( θ ) , y = pr sin( θ ) , z = p + r . 3. Section 11.6 Directional Derivative : Find the directional derivative of f ( x , y ) = 1 + 2 x y at the point (3 , 4) in the direction of v = < 4 , - 3 > . 4. Section 12.2 Double Integrals : Evaluate Z 1 0 Z 2 - x x ( x 2 - y ) dy dx 5. Section 12.8 Change of Variables in Multiple Integrals : Use the transformation u = x - y , v = x + y to evaluate " R ( x + y ) e x 2 - y 2 dA , where R is the region bounded by the lines x - y = 0 , x - y = 2 , x + y = 0 and x + y = 3. 6. Section 13.2 Line Integrals : Evaluate the line integral Z C xy 3 ds where C is given by the parametric equations x = 4 sin( t ) , y = 4 cos( t ) , z = 3 t , 0 t π/ 2. 7. Section 13.3 Conservative Vector Fields and Their Potential Functions : Verify F ( x , y ) = (4 x 3 y 2 - 3 xy 3 ) i + (2 x 4 y - 9 2 x 2 y 2 + 4 y 3 ) j is a conservative vector field. Then find a potential function f for F . 8. Section 13.4 Green’s Theorem : Use Green’s Theorem to evaluate Z C y 2 cos( x ) dx + ( x 2 + 2 y sin( x )) dy where C is the triangle from (0 , 0) to (2 , 6) to (2 , 0) to (0 , 0). 9. Section 13.6 Tangent Planes of Parametric Surfaces
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