For the following exercises, let F ( x , y) = 2xy 2 i + ( 2yx 2 +2y ) j and G(x, y) = ( y + x )i + (y — x )j, and let C 1 be the curve consisting of the circle of radius 2, centered at the origin and oriented counterclockwise, and C 2 be the curve consisting of a line segment from (0, 0) to (1, 1) followed by a line segment from (1, 1) to (3, 1). 130. Calculate the line integral of F over Ci.
For the following exercises, let F ( x , y) = 2xy 2 i + ( 2yx 2 +2y ) j and G(x, y) = ( y + x )i + (y — x )j, and let C 1 be the curve consisting of the circle of radius 2, centered at the origin and oriented counterclockwise, and C 2 be the curve consisting of a line segment from (0, 0) to (1, 1) followed by a line segment from (1, 1) to (3, 1). 130. Calculate the line integral of F over Ci.
For the following exercises, let F(x, y) = 2xy2i + (2yx2+2y)j and
G(x, y) = (y + x)i + (y — x)j, and let C1be the curve consisting of the circle of radius 2, centered at the origin and oriented counterclockwise, and C2be the curve consisting of a line segment from (0, 0) to (1, 1) followed by a line segment from (1, 1) to (3, 1).
130. Calculate the line integral of F over Ci.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Evaluate V9+x² dx+xy°dy along the positively oriented curve C where the C is the
boundary of the rectangle with vertices (0, 0), (0, 4), (2, 0), and (2, 4).
Find the distance from the point (-2, 2, 3) to the plane -3x + y – z = 9.
Use Eq. (5) to find the point P nearest to Q = (2, 1, 2) on the plane x+y+z=l.
Finite Mathematics & Its Applications (12th Edition)
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