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7. We have to find all solutions such that 
Exponentiate both sides to get 
Hence 
8. 
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8 pts.) 7. Find all solutions of in log 2 [12 pts. 8. Compute...
5. Let f(x) = e-} Log(z) (that is, f is the principal branch of z-1/2). Compute...
5. Let f(x) = e-} Log(z) (that is, f is the principal branch of z-1/2). Compute [flade, where (a) (2 points) y is the upper half of the unit circle C(0) from +1 to -1; (b) (2 points) y is the lower half of the unit circle C1(0) from +1 to -1.
where the is the circle at the origin travelles counter clockwise find dz We were unable...
where the is the circle at
the origin travelles counter clockwise find dz
We were unable to transcribe this imageWe were unable to transcribe this image(z - a) (2 -b)
please show your work 6. (20 pts) Let F = (r?, yº-roys) and C be a...
please show your work
6. (20 pts) Let F = (r?, yº-roys) and C be a unit circle centered at the origin oriented counter- clockwise. Convert F.dito a double integral over the unit upper hemisphere oriented outward and you do NOT have to evaluate the integrals. (a) (5 pts) Parametrize the upper unit upper hemisphere. (Hint: Spherical coordinates?) (b) (5 pts) Find da (c) (10 pts) Apply Stoke's Theorem to covert the integral to a double integral.
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...
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...
Problem 2a (8 pts) Suppose that the magnetic field in some region is それ (where k > 0 is a const...
Problem 2a (8 pts) Suppose that the magnetic field in some region is それ (where k > 0 is a constant). A quarter-circle wire loop of radius a is lying in the xy plane with the radius of the circle centered at the origin as shown in the diagram. A power course is applied to the loop with a constant voltage V Vo driving the current in a counter-clockwise direction as shown in the diagram. The loop has resistance R....
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...
8 pts Question 3 Consider the function f(x,y, 2)(x 1)3(y2)3 ( 1)2(y2)2(z 3)2 (a) Compute the...
8 pts Question 3 Consider the function f(x,y, 2)(x 1)3(y2)3 ( 1)2(y2)2(z 3)2 (a) Compute the increment Af if (r,y, z) changes from (1,2,3 (b) Compute the differential df for the corresponding change in position. What does (2,3,4) to this say about the point (1, 2,3)? ( 13y2)3 ( 1)2(y 2)2(z 3)2 with C (c) Consider the contour C = a constant. Use implicit differentiation to compute dz/Ox. Your answer should be a function of z. (d) Find the unit...
0/10.5 pts Question9 Charge 1 of +8 micro-coulombs is located at the origin, charge 2 of-7...
0/10.5 pts Question9 Charge 1 of +8 micro-coulombs is located at the origin, charge 2 of-7 micro-coulombs is located at x O cm, y -9 cm, and charge 3 of +5 micro-coulombs is located at x -18 cm, y 0 cm. What is the direction of the total electric force on charge 1 measured counter-clockwise from the +x axis, in degrees? 100.1247
8) Find the circulation of F =(6x+5 y,4y+3z, 2x+1z) around a square of side 7, centered at (1,2,1), lying in the pla...
8) Find the circulation of F =(6x+5 y,4y+3z, 2x+1z) around a square of side 7, centered at (1,2,1), lying in the plane 4x+1y+6z = 12 , and oriented clockwise when viewed from the origin
8) Find the circulation of F =(6x+5 y,4y+3z, 2x+1z) around a square of side 7, centered at (1,2,1), lying in the plane 4x+1y+6z = 12 , and oriented clockwise when viewed from the origin
5. Let f(x) = e-} Log(z) (that is, f is the principal branch of z-1/2). Compute [flade, where (a) (2 points) y is the upper half of the unit circle C(0) from +1 to -1; (b) (2 points) y is the lower half of the unit circle C1(0) from +1 to -1.
where the is the circle at
the origin travelles counter clockwise find dz
We were unable to transcribe this imageWe were unable to transcribe this image(z - a) (2 -b)
please show your work
6. (20 pts) Let F = (r?, yº-roys) and C be a unit circle centered at the origin oriented counter- clockwise. Convert F.dito a double integral over the unit upper hemisphere oriented outward and you do NOT have to evaluate the integrals. (a) (5 pts) Parametrize the upper unit upper hemisphere. (Hint: Spherical coordinates?) (b) (5 pts) Find da (c) (10 pts) Apply Stoke's Theorem to covert the integral to a double integral.
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...
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...
Problem 2a (8 pts) Suppose that the magnetic field in some region is それ (where k > 0 is a constant). A quarter-circle wire loop of radius a is lying in the xy plane with the radius of the circle centered at the origin as shown in the diagram. A power course is applied to the loop with a constant voltage V Vo driving the current in a counter-clockwise direction as shown in the diagram. The loop has resistance R....
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...
8 pts Question 3 Consider the function f(x,y, 2)(x 1)3(y2)3 ( 1)2(y2)2(z 3)2 (a) Compute the increment Af if (r,y, z) changes from (1,2,3 (b) Compute the differential df for the corresponding change in position. What does (2,3,4) to this say about the point (1, 2,3)? ( 13y2)3 ( 1)2(y 2)2(z 3)2 with C (c) Consider the contour C = a constant. Use implicit differentiation to compute dz/Ox. Your answer should be a function of z. (d) Find the unit...
0/10.5 pts Question9 Charge 1 of +8 micro-coulombs is located at the origin, charge 2 of-7 micro-coulombs is located at x O cm, y -9 cm, and charge 3 of +5 micro-coulombs is located at x -18 cm, y 0 cm. What is the direction of the total electric force on charge 1 measured counter-clockwise from the +x axis, in degrees? 100.1247
8) Find the circulation of F =(6x+5 y,4y+3z, 2x+1z) around a square of side 7, centered at (1,2,1), lying in the plane 4x+1y+6z = 12 , and oriented clockwise when viewed from the origin
8) Find the circulation of F =(6x+5 y,4y+3z, 2x+1z) around a square of side 7, centered at (1,2,1), lying in the plane 4x+1y+6z = 12 , and oriented clockwise when viewed from the origin
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