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Problem 4 (15 points) Calculate xe ² ds Jc where C is a piecewise linear path...
7. (10 points) Consider the linear path "C" in the xy-plane from the point (1,1) to...
7. (10 points) Consider the linear path "C" in the xy-plane from the point (1,1) to the point (2,3). (a) Find an appropriate vector valued function r(t) along with an appropriate interval a <t<b which describes the path C. (b) Evaluate the line integral 2xy ds where C is the curve you found above.
(2) This is problem 3 from the homework 9. Let F = 2.xyzi + x2zj +...
(2) This is problem 3 from the homework 9. Let F = 2.xyzi + x2zj + ryk. Show that F is conservative. Find f such that VS = F (do not guess, use formula) and evaluate F. ds where c is a piecewise smooth curve from the point (1,1,1) to the point (1, 2, 4). F
c) fox2y2 dx - xy3 dy, where C is the triangle with vertices (0, 0), (1,...
c) fox2y2 dx - xy3 dy, where C is the triangle with vertices (0, 0), (1, 0), (1, 1). (CE. Lect 08) Our goal is to evaluate the line integral in No. 3 (c), p. 279 of Kaplan (the last part of this question). The path involved is a triangle. To calculate such a line integral, we break up its path into pieces (hence the first three parts of this question). At the end, we add the pieces together. (a)...
QB(27pts)(a). Evaluate the circulation ofF(xy)-<x,y+x> on the curve r(t)=<2cost, 2sinp, foross2n (b) Evaluate J F.dr, where C is a piecewise smooth path from (1,0) to (2,1) and F- (e'...
QB(27pts)(a). Evaluate the circulation ofF(xy)-<x,y+x> on the curve r(t)=<2cost, 2sinp, foross2n (b) Evaluate J F.dr, where C is a piecewise smooth path from (1,0) to (2,1) and F- (e'cos x)i +(e'sinx)j [Hint: Test F for conservative (c). Use green theorem to express the line integral as a double integral and then evaluate. where C is the circle x+y-4 with counterclockwise orientation. (d(Bonus10 pts) Consider the vector field Foxyz) a. Find curl F y, ,z> F.dr where C is the curve...
Problem 4 Shortest Path Problem-15 points You are in the market for a new car and...
Problem 4 Shortest Path Problem-15 points You are in the market for a new car and a new car costs $10,000. The annual operating costs and resale value of a used car are shown in the Table below. e of Car (Years) Resale Value (S) Costs (S) 300 (year 1) 500 (year 2) 800 (year 3) 1200 (year 4 1600 (year 5) 2200 (year 6) 8000 6000 5000 3000 1500 Assuming that you now have a new car, determine a...
Problem 1. (16.2 Line Integrals) Evaluate the line integral Jc xeids, where C is the line segment from (0,0,0) to (1.2,3).(t,at,3t) Problem 1. (16.2 Line Integrals) Evaluate the line integra...
Problem 1. (16.2 Line Integrals) Evaluate the line integral Jc xeids, where C is the line segment from (0,0,0) to (1.2,3).(t,at,3t)
Problem 1. (16.2 Line Integrals) Evaluate the line integral Jc xeids, where C is the line segment from (0,0,0) to (1.2,3).(t,at,3t)
4. -15 points Use Green's theorem for flux to evaluate the line integra ds . (6ху, y2-x2) and C i...
4. -15 points Use Green's theorem for flux to evaluate the line integra ds . (6ху, y2-x2) and C is the positively oriented boundary curve of the region bounded by y F 0 and y x(4-x). Submit Answer
4. -15 points Use Green's theorem for flux to evaluate the line integra ds . (6ху, y2-x2) and C is the positively oriented boundary curve of the region bounded by y F 0 and y x(4-x). Submit Answer
(10) (8 points) Evaluate the line integral Scry ds, where C is the upper half of...
(10) (8 points) Evaluate the line integral Scry ds, where C is the upper half of the circle r2 + y2 = 4.
Consider the following C: line segments from (0, 1) to (0, 4) and (0, 4) to (3, 3) (a) Find a parametrization of the path C. 3,53 r(t) (b) Evaluate (4x + 9y ds. Consider the following C: line se...
Consider the following C: line segments from (0, 1) to (0, 4) and (0, 4) to (3, 3) (a) Find a parametrization of the path C. 3,53 r(t) (b) Evaluate (4x + 9y ds.
Consider the following C: line segments from (0, 1) to (0, 4) and (0, 4) to (3, 3) (a) Find a parametrization of the path C. 3,53 r(t) (b) Evaluate (4x + 9y ds.
Problem 1 Evaluate the line integral / x2 ds, where C is the line segment from...
Problem 1 Evaluate the line integral / x2 ds, where C is the line segment from (3,0) to (0,4) in the xy-plane.
7. (10 points) Consider the linear path "C" in the xy-plane from the point (1,1) to the point (2,3). (a) Find an appropriate vector valued function r(t) along with an appropriate interval a <t<b which describes the path C. (b) Evaluate the line integral 2xy ds where C is the curve you found above.
(2) This is problem 3 from the homework 9. Let F = 2.xyzi + x2zj + ryk. Show that F is conservative. Find f such that VS = F (do not guess, use formula) and evaluate F. ds where c is a piecewise smooth curve from the point (1,1,1) to the point (1, 2, 4). F
c) fox2y2 dx - xy3 dy, where C is the triangle with vertices (0, 0), (1, 0), (1, 1). (CE. Lect 08) Our goal is to evaluate the line integral in No. 3 (c), p. 279 of Kaplan (the last part of this question). The path involved is a triangle. To calculate such a line integral, we break up its path into pieces (hence the first three parts of this question). At the end, we add the pieces together. (a)...
QB(27pts)(a). Evaluate the circulation ofF(xy)-<x,y+x> on the curve r(t)=<2cost, 2sinp, foross2n (b) Evaluate J F.dr, where C is a piecewise smooth path from (1,0) to (2,1) and F- (e'cos x)i +(e'sinx)j [Hint: Test F for conservative (c). Use green theorem to express the line integral as a double integral and then evaluate. where C is the circle x+y-4 with counterclockwise orientation. (d(Bonus10 pts) Consider the vector field Foxyz) a. Find curl F y, ,z> F.dr where C is the curve...
Problem 4 Shortest Path Problem-15 points You are in the market for a new car and a new car costs $10,000. The annual operating costs and resale value of a used car are shown in the Table below. e of Car (Years) Resale Value (S) Costs (S) 300 (year 1) 500 (year 2) 800 (year 3) 1200 (year 4 1600 (year 5) 2200 (year 6) 8000 6000 5000 3000 1500 Assuming that you now have a new car, determine a...
Problem 1. (16.2 Line Integrals) Evaluate the line integral Jc xeids, where C is the line segment from (0,0,0) to (1.2,3).(t,at,3t)
Problem 1. (16.2 Line Integrals) Evaluate the line integral Jc xeids, where C is the line segment from (0,0,0) to (1.2,3).(t,at,3t)
4. -15 points Use Green's theorem for flux to evaluate the line integra ds . (6ху, y2-x2) and C is the positively oriented boundary curve of the region bounded by y F 0 and y x(4-x). Submit Answer
4. -15 points Use Green's theorem for flux to evaluate the line integra ds . (6ху, y2-x2) and C is the positively oriented boundary curve of the region bounded by y F 0 and y x(4-x). Submit Answer
(10) (8 points) Evaluate the line integral Scry ds, where C is the upper half of the circle r2 + y2 = 4.
Consider the following C: line segments from (0, 1) to (0, 4) and (0, 4) to (3, 3) (a) Find a parametrization of the path C. 3,53 r(t) (b) Evaluate (4x + 9y ds.
Consider the following C: line segments from (0, 1) to (0, 4) and (0, 4) to (3, 3) (a) Find a parametrization of the path C. 3,53 r(t) (b) Evaluate (4x + 9y ds.
Problem 1 Evaluate the line integral / x2 ds, where C is the line segment from (3,0) to (0,4) in the xy-plane.
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