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Unformatted text preview: 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 , given u = x 2 + yz , x = pr cos( ) , y = pr sin( ) , 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 = &lt; 4 ,- 3 &gt; . 4. Section 12.2 Double Integrals : Evaluate Z 1 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 &quot; R ( x + y ) e x 2- y 2 dA , where R is the region bounded by the lines x- y = , x- y = 2 , x + y = 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 , t / 2....
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This note was uploaded on 05/15/2011 for the course ENGR 120 taught by Professor Staff during the Spring '11 term at Washington State University .
- Spring '11