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1. Consider the definite integralZcoswhere lal 2π 0 1+a2-2acos(x) a. (1 point) Using the change of...
(1 point) The following sum 5n n TI is a right Riemann sum for a certain definite integral f(x) dz using a partition of the interval [1, b] into n subintervals of equal length. Then the upper limit o...
(1 point) The following sum 5n n TI is a right Riemann sum for a certain definite integral f(x) dz using a partition of the interval [1, b] into n subintervals of equal length. Then the upper limit of integration must be: b6 and the integrand must be the function f(a)
(1 point) The following sum 5n n TI is a right Riemann sum for a certain definite integral f(x) dz using a partition of the interval [1, b] into...
10. Let F(x, y, z) = 〈y,-z, 10) per half of x2 +y2 + z2 = 1, oriented upward, and C the circle 2 y 1 in the z - y plane, oriented counter-clockwise. Find Jscurl(F) ndS directly and by using Stokes&#...
10. Let F(x, y, z) = 〈y,-z, 10) per half of x2 +y2 + z2 = 1, oriented upward, and C the circle 2 y 1 in the z - y plane, oriented counter-clockwise. Find Jscurl(F) ndS directly and by using Stokes' Theorem. , where S is the up
10. Let F(x, y, z) = 〈y,-z, 10) per half of x2 +y2 + z2 = 1, oriented upward, and C the circle 2 y 1 in the z - y...
1. (1 point) Find the arc-length parametrization of the curve that is the intersection of the elliptic cylr 1 and the plane z-2y = 7. Use s as the arc length parameter with s = 0 corresponding to...
1. (1 point) Find the arc-length parametrization of the curve that is the intersection of the elliptic cylr 1 and the plane z-2y = 7. Use s as the arc length parameter with s = 0 corresponding to the point (0, 1.9) oriented counter-clockwise as seen from above Spring 2016)
1. (1 point) Find the arc-length parametrization of the curve that is the intersection of the elliptic cylr 1 and the plane z-2y = 7. Use s as the arc...
Find an expression as a definite integral for the length of an ellipse x2/a2+y2/b2= 1 by using th...
Find an expression as a definite integral for the length of an ellipse x2/a2+y2/b2= 1 by using the parametrization x=a sinφ, y= b cosφ and letting you should get We were unable to transcribe this image1-k2sin2 od 1-k2sin2 od
7. Use Green's Theorem to find Jc F.nds, where C is the boundary of the region bounded by y = 4-x2 and y = 0, oriented counter-clockwise and F(x,y) = (y,-3z). what about if F(r, y) (2,3)? x2...
7. Use Green's Theorem to find Jc F.nds, where C is the boundary of the region bounded by y = 4-x2 and y = 0, oriented counter-clockwise and F(x,y) = (y,-3z). what about if F(r, y) (2,3)? x2 + y2 that lies inside x2 + y2-1. Find the surface area of this 8. Consider the part of z surface. 9. Use Green's Theorem to find Find J F Tds, where F(x, y) (ry,e"), and C consists of the line segment...
1. (1 point) Find the arc-length parametrization of the curve that is the intersection of the...
1. (1 point) Find the arc-length parametrization of the curve that is the intersection of the elliptic cylinder -+ y1 and the plane z - 2y -7. Use s as the arc-length parameter with s 0 corresponding to the point (0, 1,9) oriented counter-clockwise as seen from above.
(1 point) Use part I of the Fundamental Theorem of Calculus to find the derivative of (1 point) If f(x) dx 21 and...
(1 point) Use part I of the Fundamental Theorem of Calculus to find the derivative of (1 point) If f(x) dx 21 and g(x) dz 16, find [4f(z) +6g(a)] dz. Answer: 164
(1 point) Use part I of the Fundamental Theorem of Calculus to find the derivative of
(1 point) If f(x) dx 21 and g(x) dz 16, find [4f(z) +6g(a)] dz. Answer: 164
Previous ProblemPlUDIelfLis (1 point) You are given the four points in the plane A (1,1), B- (4,-2), C (7,2), and D The graph of the function f(z) consists of the three line segments AB, BC and CD...
Previous ProblemPlUDIelfLis (1 point) You are given the four points in the plane A (1,1), B- (4,-2), C (7,2), and D The graph of the function f(z) consists of the three line segments AB, BC and CD (11, -2) Find the integralf() dz by interpreting the integral in terms of sums and/or differences of areas of elementary figures f(z) de-
Previous ProblemPlUDIelfLis (1 point) You are given the four points in the plane A (1,1), B- (4,-2), C (7,2), and...
(6) Show that F(x, y) = (x+y)i + (**)is conservative. (a) Then find such that S...
(6) Show that F(x, y) = (x+y)i + (**)is conservative. (a) Then find such that S = F (potential function). (5) Use the results in part(a) to cakulae ( F. ds along C which the curve y = a* from (0,0) to (2,16). (2) Use Green's Theorem to evaluate 1. F. ds. F(1,y) =(yº+sin(26))i + (2xy2 + cos y)and C is the unit circle oriented counter clockwise (6) Evaluate the surface integral || 9. ds. F(x,y,z) = xi +++where S...
Log(2+5) 1. Consider function f(z) sin 2 (a) Determine all singular point (s) of f enclosed...
Log(2+5) 1. Consider function f(z) sin 2 (a) Determine all singular point (s) of f enclosed in the circle C4(0) (b) Are they isolated singularities? If so, which kind of isolated singularity are they (remov- able, pole, essential)? (c) Compute the residue of f at each of these singularities (d) Evaluate the integral f f(2)dz where y is the circle Ca(0) oriented counterclockwise 1.0 0.5 -0.5 Answer key 1. (а) z0,-T, T (b) Yes. Each is a pole of order...
(1 point) The following sum 5n n TI is a right Riemann sum for a certain definite integral f(x) dz using a partition of the interval [1, b] into n subintervals of equal length. Then the upper limit of integration must be: b6 and the integrand must be the function f(a)
(1 point) The following sum 5n n TI is a right Riemann sum for a certain definite integral f(x) dz using a partition of the interval [1, b] into...
10. Let F(x, y, z) = 〈y,-z, 10) per half of x2 +y2 + z2 = 1, oriented upward, and C the circle 2 y 1 in the z - y plane, oriented counter-clockwise. Find Jscurl(F) ndS directly and by using Stokes' Theorem. , where S is the up
10. Let F(x, y, z) = 〈y,-z, 10) per half of x2 +y2 + z2 = 1, oriented upward, and C the circle 2 y 1 in the z - y...
1. (1 point) Find the arc-length parametrization of the curve that is the intersection of the elliptic cylr 1 and the plane z-2y = 7. Use s as the arc length parameter with s = 0 corresponding to the point (0, 1.9) oriented counter-clockwise as seen from above Spring 2016)
1. (1 point) Find the arc-length parametrization of the curve that is the intersection of the elliptic cylr 1 and the plane z-2y = 7. Use s as the arc...
7. Use Green's Theorem to find Jc F.nds, where C is the boundary of the region bounded by y = 4-x2 and y = 0, oriented counter-clockwise and F(x,y) = (y,-3z). what about if F(r, y) (2,3)? x2 + y2 that lies inside x2 + y2-1. Find the surface area of this 8. Consider the part of z surface. 9. Use Green's Theorem to find Find J F Tds, where F(x, y) (ry,e"), and C consists of the line segment...
1. (1 point) Find the arc-length parametrization of the curve that is the intersection of the elliptic cylinder -+ y1 and the plane z - 2y -7. Use s as the arc-length parameter with s 0 corresponding to the point (0, 1,9) oriented counter-clockwise as seen from above.
(1 point) Use part I of the Fundamental Theorem of Calculus to find the derivative of (1 point) If f(x) dx 21 and g(x) dz 16, find [4f(z) +6g(a)] dz. Answer: 164
(1 point) Use part I of the Fundamental Theorem of Calculus to find the derivative of
(1 point) If f(x) dx 21 and g(x) dz 16, find [4f(z) +6g(a)] dz. Answer: 164
Previous ProblemPlUDIelfLis (1 point) You are given the four points in the plane A (1,1), B- (4,-2), C (7,2), and D The graph of the function f(z) consists of the three line segments AB, BC and CD (11, -2) Find the integralf() dz by interpreting the integral in terms of sums and/or differences of areas of elementary figures f(z) de-
Previous ProblemPlUDIelfLis (1 point) You are given the four points in the plane A (1,1), B- (4,-2), C (7,2), and...
(6) Show that F(x, y) = (x+y)i + (**)is conservative. (a) Then find such that S = F (potential function). (5) Use the results in part(a) to cakulae ( F. ds along C which the curve y = a* from (0,0) to (2,16). (2) Use Green's Theorem to evaluate 1. F. ds. F(1,y) =(yº+sin(26))i + (2xy2 + cos y)and C is the unit circle oriented counter clockwise (6) Evaluate the surface integral || 9. ds. F(x,y,z) = xi +++where S...
Log(2+5) 1. Consider function f(z) sin 2 (a) Determine all singular point (s) of f enclosed in the circle C4(0) (b) Are they isolated singularities? If so, which kind of isolated singularity are they (remov- able, pole, essential)? (c) Compute the residue of f at each of these singularities (d) Evaluate the integral f f(2)dz where y is the circle Ca(0) oriented counterclockwise 1.0 0.5 -0.5 Answer key 1. (а) z0,-T, T (b) Yes. Each is a pole of order...
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