14th - a ) Directly b ) Using Green’s Theorem 6. Use...

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MATH 120 WEEK 14 (RECITATION QUESTIONS) 1. Determine whether or not F ( x,y ) = ( x 3 + 4 xy ) i + (4 xy - y 3 ) j is a conservative vector field.If it is, find a function f such that F = f 2. (a) Find a function f such that F = f and (b) Use part (a) to evaluate R C F d r along the given curve C . where i ) F ( x,y ) = x 3 y 4 i + x 4 y 3 j and C : r ( t ) = t i + (1 + t 3 ) j , 0 t 1 ii ) F ( x,y,z ) = (2 xz + y 2 ) i + 2 xy j + ( x 2 + 3 z 2 ) k and C : x = t 2 , y = t + 1 , z = 2 t - 1, 0 t 1 3. (If time permits)Show that the line integral is independent of path and evaluate the integral Z C (1 - ye - x ) dx + e - x dy C is any path from (0 , 1) to (1 , 2) 4. Find the work done by the force field F in moving an object from P to Q where F ( x,y ) = ( y 2 /x 2 ) i - (2 y/x ) j ; P (1 , 1) , Q (4 , - 2) 5. Evaluate the line integral I C y dx - x dy where C is the circle with center the origin and radius 1, by two methods
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Unformatted text preview: a ) Directly b ) Using Green’s Theorem 6. Use Green’s Theorem to evaluate R C F • d r .(Check the orientation of the curve before applying the theorem.) F ( x,y ) = h √ x + y 3 ,x 2 + √ y i , C consists of the arc of the curve y = sin x from (0 , 0) to ( π, 0) and the line segment from ( π, 0) to (0 , 0) 7. Use Green’s Theorem to find the work done by the force F ( x,y ) = x ( x + y ) i + xy 2 j in moving a particle from the origin along the x-axis to (1 , 0), then along the line segment to (0 , 1), and then back to the origin along the y-axis. 1...
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