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6. Consider a triangle with vertices at 1, 2 + 2i, 3-i oriented clockwise. (a) Draw...
Find parameterisations x(t), y(t), t є 1 (a) (b) (c) for each of the following curves: 2. The straight line from 4+2i to 3+5i; The circle of radius 2 centered at 3-i oriented counter-clockwise; The g...
Find parameterisations x(t), y(t), t є 1 (a) (b) (c) for each of the following curves: 2. The straight line from 4+2i to 3+5i; The circle of radius 2 centered at 3-i oriented counter-clockwise; The graph of the cosine function over the interval [π/4,2n
Find parameterisations x(t), y(t), t є 1 (a) (b) (c) for each of the following curves: 2. The straight line from 4+2i to 3+5i; The circle of radius 2 centered at 3-i oriented counter-clockwise; The graph...
do the three with mark 1.31. Show that the union of two regions with nonempty intersection...
do the three with mark
1.31. Show that the union of two regions with nonempty intersection is itself a region. 1.32. Show that if ACB and B is closed, then dAC B. Similarly, if AC B and A is open, show that A is contained in the interior of B 1.33. Find a parametrization for each of the following paths: (a) the circle C[1+ i, 1], oriented counter-clockwise (b) the line segment from -1-to 2 (c) the top half of...
6. (1 point) Use Stokes' Theorem to find the line integral /2y dx + dy + (4-3x) dz, where C is the boundary of the triangle with vertices (0,0,0), (1,3,-2), and -2,4,5), oriented counterclockwise...
6. (1 point) Use Stokes' Theorem to find the line integral /2y dx + dy + (4-3x) dz, where C is the boundary of the triangle with vertices (0,0,0), (1,3,-2), and -2,4,5), oriented counterclockwise as viewed from the point (1, 0, 0)
6. (1 point) Use Stokes' Theorem to find the line integral /2y dx + dy + (4-3x) dz, where C is the boundary of the triangle with vertices (0,0,0), (1,3,-2), and -2,4,5), oriented counterclockwise as viewed from the...
I sinta fosinta 3. (40 points) Evaluate the following integrals: (a) (10 points) sin(2 + 7)dz,...
I sinta fosinta 3. (40 points) Evaluate the following integrals: (a) (10 points) sin(2 + 7)dz, where C is the square with vertices at 2i, 3i, 1+ 3i and 1+2i, in this order. (b) (10 points) sin(22) $c 2+1 where C is the positively oriented (counter-clockwise) triangle with vertices (0,0), (2,0) and (0,5). (c) (10 points) cosh(22) -dz, (3-2) where is the negatively oriented (clockwise) circle centered at (1,1) of radius 2. (d) (10 points) dz, 2-1 where C consist...
The parametric equations where 0 tl describe the line segment that joins the points P1(x1, y and P2(x2, y2) Use a graphing device to draw the triangle with vertices A(1, 1), B(3, 4), C(1,7). Find the...
The parametric equations where 0 tl describe the line segment that joins the points P1(x1, y and P2(x2, y2) Use a graphing device to draw the triangle with vertices A(1, 1), B(3, 4), C(1,7). Find the parametrization, including endpoints, and sketch to check. (Enter your answers as a comma- separated list of equations. Let x and y be in terms of t.) A to B B to C A to C
The parametric equations where 0 tl describe the line...
(5) Use Cauchy Integral Formula to calculateh(2+(i+1), ee is whose vertices are 0, 4, 2- 2i,...
(5) Use Cauchy Integral Formula to calculateh(2+(i+1), ee is whose vertices are 0, 4, 2- 2i, and -2i. oriented counterclockwise. Assume a suitable branch of (z +4i) c (2+ I)2 + i dz where C is the paralle 5)
True or False Determine whet her the statement is true or false, and circle the correct answer. Each question is worth 2 points. (1) If F is a vector field and C is an oriented curve, then F dr must...
True or False Determine whet her the statement is true or false, and circle the correct answer. Each question is worth 2 points. (1) If F is a vector field and C is an oriented curve, then F dr must be less than zero. F (2) It is possible that for a certain vector field F and piecewise smooth oriented path C we have/. F. dr-2i-Sj. (3) Suppose d·is the unit square joining the points (0,0), (1,0), (1,1), (0.1) oriented...
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)...
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.
Suppose that we have a graph with vertices 1, 2, 3, 4, 5, 6, 7 and...
Suppose that we have a graph with vertices 1, 2, 3, 4, 5, 6, 7 and edges (1, 5), (2, 5), (3, 4), (3, 5), (6, 2), (7, 1), (7, 4). Draw this graph and execute the function mexset1) to find the number of vertices in the largest independent set of the graph. What is the best way to choose v' for executing this function? Must draw a tree structure to show how you come up with the answer.
Find parameterisations x(t), y(t), t є 1 (a) (b) (c) for each of the following curves: 2. The straight line from 4+2i to 3+5i; The circle of radius 2 centered at 3-i oriented counter-clockwise; The graph of the cosine function over the interval [π/4,2n
Find parameterisations x(t), y(t), t є 1 (a) (b) (c) for each of the following curves: 2. The straight line from 4+2i to 3+5i; The circle of radius 2 centered at 3-i oriented counter-clockwise; The graph...
do the three with mark
1.31. Show that the union of two regions with nonempty intersection is itself a region. 1.32. Show that if ACB and B is closed, then dAC B. Similarly, if AC B and A is open, show that A is contained in the interior of B 1.33. Find a parametrization for each of the following paths: (a) the circle C[1+ i, 1], oriented counter-clockwise (b) the line segment from -1-to 2 (c) the top half of...
6. (1 point) Use Stokes' Theorem to find the line integral /2y dx + dy + (4-3x) dz, where C is the boundary of the triangle with vertices (0,0,0), (1,3,-2), and -2,4,5), oriented counterclockwise as viewed from the point (1, 0, 0)
6. (1 point) Use Stokes' Theorem to find the line integral /2y dx + dy + (4-3x) dz, where C is the boundary of the triangle with vertices (0,0,0), (1,3,-2), and -2,4,5), oriented counterclockwise as viewed from the...
I sinta fosinta 3. (40 points) Evaluate the following integrals: (a) (10 points) sin(2 + 7)dz, where C is the square with vertices at 2i, 3i, 1+ 3i and 1+2i, in this order. (b) (10 points) sin(22) $c 2+1 where C is the positively oriented (counter-clockwise) triangle with vertices (0,0), (2,0) and (0,5). (c) (10 points) cosh(22) -dz, (3-2) where is the negatively oriented (clockwise) circle centered at (1,1) of radius 2. (d) (10 points) dz, 2-1 where C consist...
The parametric equations where 0 tl describe the line segment that joins the points P1(x1, y and P2(x2, y2) Use a graphing device to draw the triangle with vertices A(1, 1), B(3, 4), C(1,7). Find the parametrization, including endpoints, and sketch to check. (Enter your answers as a comma- separated list of equations. Let x and y be in terms of t.) A to B B to C A to C
The parametric equations where 0 tl describe the line...
(5) Use Cauchy Integral Formula to calculateh(2+(i+1), ee is whose vertices are 0, 4, 2- 2i, and -2i. oriented counterclockwise. Assume a suitable branch of (z +4i) c (2+ I)2 + i dz where C is the paralle 5)
True or False Determine whet her the statement is true or false, and circle the correct answer. Each question is worth 2 points. (1) If F is a vector field and C is an oriented curve, then F dr must be less than zero. F (2) It is possible that for a certain vector field F and piecewise smooth oriented path C we have/. F. dr-2i-Sj. (3) Suppose d·is the unit square joining the points (0,0), (1,0), (1,1), (0.1) oriented...
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)...
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.
Suppose that we have a graph with vertices 1, 2, 3, 4, 5, 6, 7 and edges (1, 5), (2, 5), (3, 4), (3, 5), (6, 2), (7, 1), (7, 4). Draw this graph and execute the function mexset1) to find the number of vertices in the largest independent set of the graph. What is the best way to choose v' for executing this function? Must draw a tree structure to show how you come up with the answer.
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