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Homework Answers
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2. (a) Evaluate the contour integral z dz, where I is the circle 12 – 11...
2. (a) Evaluate the contour integral z dz, where I is the circle 12 – 11 = 2 traversed once counterclockwise.
2 +1 (b) Evaluate the contour integral dz, 22 – 9 where I is the boundary...
2 +1 (b) Evaluate the contour integral dz, 22 – 9 where I is the boundary of the square D = {z E C:-4 < Re(z) < 4, -4 < Im(z) < 4} traversed once counterclockwise.
1 3. Let f(x) = 22(2-2)(2 - 4) and C a circle of radius 2k -...
1 3. Let f(x) = 22(2-2)(2 - 4) and C a circle of radius 2k - 1 about the origin with counterclockwise orientation. (1) Find (2) Find 50, 5(=dz. Je_1(a) dz. 5. 1(a) dz. (3) Find
(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)
(1) Evaluate the integral (r-1) min(a, y) dy dr, Jo Jo where min(x, y) is the minimum value of r ...
q2 please
(1) Evaluate the integral (r-1) min(a, y) dy dr, Jo Jo where min(x, y) is the minimum value of r and y. (2) Let f,g : R → R be functions of one variable such that f" and g" are continuous. Show that (f"(x)-g"(y)) dydx = f(0) + g(0)-f(2)-9(2) + 2f'(2) + 2g'(0). o Jo (3) Let a > 0. In spherical coordinates, a surface is defined by r = 2acos φ for 0 φ 1. Find the...
Please only do 8. 7. Compute fr Re zdz along the directed line segment lL llomん 8. Let C be the perimeter of the square with vertices at the points z = 0, z = 1, z = 1 + i, and z = i traversed once...
Please only do 8.
7. Compute fr Re zdz along the directed line segment lL llomん 8. Let C be the perimeter of the square with vertices at the points z = 0, z = 1, z = 1 + i, and z = i traversed once in that order. Show that ez dz = 0. 1, where
7. Compute fr Re zdz along the directed line segment lL llomん 8. Let C be the perimeter of the square with...
16.11. Let y be the unit circle [2] = 1 traversed twice in the clockwise direction....
16.11. Let y be the unit circle [2] = 1 traversed twice in the clockwise direction. Evaluate (a). / Log (2+2)dz, (b). / 2011
(6 inarks) Show that| 3: dlsīwhere C is the arc of the circle s|-2onthe right half d where C is the arc of the circle 2 on the right half plane 7 from :,--2i to 웡 = 2i. (6 inarks) Show that...
(6 inarks) Show that| 3: dlsīwhere C is the arc of the circle s|-2onthe right half d where C is the arc of the circle 2 on the right half plane 7 from :,--2i to 웡 = 2i.
(6 inarks) Show that| 3: dlsīwhere C is the arc of the circle s|-2onthe right half d where C is the arc of the circle 2 on the right half plane 7 from :,--2i to 웡 = 2i.
c. Evaluate ,f(z) dz with า the circle of radius 1 centered at the origin and...
c. Evaluate ,f(z) dz with า the circle of radius 1 centered at the origin and traveled once counterclockwise ˊ们: (1-2 For real twith-1 < t < 1 and +12)-1 Explain why f(:)) has an expansion of the form in C , let f(z) be defined by fG)- a. b. Compute Uo(t), Ui(t), and Uz(t) in terms of t. c. Recalling that t is a real number smaller than 1 in absolute value, find the radius of convergence of this...
19.2. Let f : [a,b] → R be integrable. Show that rb 72 (r)dz, un 0O i=1 where a, b > 0 and h (b/a...
19.2. Let f : [a,b] → R be integrable. Show that rb 72 (r)dz, un 0O i=1 where a, b > 0 and h (b/a)1/n. In particular, calculate J-3r2dr by consid- ering a partition P which divides the interval [2, 3] into n parts in geometric progression at the points 2, 2h, 2h2,2h3,... ,2h"-1,2h" -3
19.2. Let f : [a,b] → R be integrable. Show that rb 72 (r)dz, un 0O i=1 where a, b > 0 and h (b/a)1/n....
2. (a) Evaluate the contour integral z dz, where I is the circle 12 – 11 = 2 traversed once counterclockwise.
2 +1 (b) Evaluate the contour integral dz, 22 – 9 where I is the boundary of the square D = {z E C:-4 < Re(z) < 4, -4 < Im(z) < 4} traversed once counterclockwise.
1 3. Let f(x) = 22(2-2)(2 - 4) and C a circle of radius 2k - 1 about the origin with counterclockwise orientation. (1) Find (2) Find 50, 5(=dz. Je_1(a) dz. 5. 1(a) dz. (3) Find
(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)
q2 please
(1) Evaluate the integral (r-1) min(a, y) dy dr, Jo Jo where min(x, y) is the minimum value of r and y. (2) Let f,g : R → R be functions of one variable such that f" and g" are continuous. Show that (f"(x)-g"(y)) dydx = f(0) + g(0)-f(2)-9(2) + 2f'(2) + 2g'(0). o Jo (3) Let a > 0. In spherical coordinates, a surface is defined by r = 2acos φ for 0 φ 1. Find the...
Please only do 8.
7. Compute fr Re zdz along the directed line segment lL llomん 8. Let C be the perimeter of the square with vertices at the points z = 0, z = 1, z = 1 + i, and z = i traversed once in that order. Show that ez dz = 0. 1, where
7. Compute fr Re zdz along the directed line segment lL llomん 8. Let C be the perimeter of the square with...
16.11. Let y be the unit circle [2] = 1 traversed twice in the clockwise direction. Evaluate (a). / Log (2+2)dz, (b). / 2011
(6 inarks) Show that| 3: dlsīwhere C is the arc of the circle s|-2onthe right half d where C is the arc of the circle 2 on the right half plane 7 from :,--2i to 웡 = 2i.
(6 inarks) Show that| 3: dlsīwhere C is the arc of the circle s|-2onthe right half d where C is the arc of the circle 2 on the right half plane 7 from :,--2i to 웡 = 2i.
c. Evaluate ,f(z) dz with า the circle of radius 1 centered at the origin and traveled once counterclockwise ˊ们: (1-2 For real twith-1 < t < 1 and +12)-1 Explain why f(:)) has an expansion of the form in C , let f(z) be defined by fG)- a. b. Compute Uo(t), Ui(t), and Uz(t) in terms of t. c. Recalling that t is a real number smaller than 1 in absolute value, find the radius of convergence of this...
19.2. Let f : [a,b] → R be integrable. Show that rb 72 (r)dz, un 0O i=1 where a, b > 0 and h (b/a)1/n. In particular, calculate J-3r2dr by consid- ering a partition P which divides the interval [2, 3] into n parts in geometric progression at the points 2, 2h, 2h2,2h3,... ,2h"-1,2h" -3
19.2. Let f : [a,b] → R be integrable. Show that rb 72 (r)dz, un 0O i=1 where a, b > 0 and h (b/a)1/n....
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