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Problem 5: Evaluate: sin #2? + cos2 9 (2-1)(2-2) where C is the circle z =...
Q5) Evaluate $c f(z) dz where C is the unit circle Iz| = 1 and f(2)...
Q5) Evaluate $c f(z) dz where C is the unit circle Iz| = 1 and f(2) is defined as follows a) f(z) = z2+z2+z_ b) f(x) = tan z c) f() = cosha
1. a) Substitute u = sin(x) to evaluate sin^2(x) cos^3(x) dx. [trig identity sin2(x)+cos2(x) = 1]....
1. a) Substitute u = sin(x) to evaluate sin^2(x) cos^3(x) dx. [trig identity sin2(x)+cos2(x) = 1]. b) Find the antiderivatives: i) sin(2x) dx ii) (cos(4x)+3x^2) dx
1. Evaluate the integral of f(r, θ, φ)-1 + r2 cos2( over a sphere of radius h. (Hint: we did most...
1. Evaluate the integral of f(r, θ, φ)-1 + r2 cos2( over a sphere of radius h. (Hint: we did most of this problem in class; 9) sin φ
1. Evaluate the integral of f(r, θ, φ)-1 + r2 cos2( over a sphere of radius h. (Hint: we did most of this problem in class; 9) sin φ
Evaluate Sc (2+2)dy where C is described by parametric equations x(t) = cos(t), y= sin(t), z...
Evaluate Sc (2+2)dy where C is described by parametric equations x(t) = cos(t), y= sin(t), z = 2,0 <t< Select one: O A. +2 O B. 1+2 O C.-1 OD. -1 ABC is a triangle in R where A =(1,4,5), B =(2,-1,0) and C =(4, 2, -3). Find the area of ABC. Select one: O A. (-30,7, -13) O B. -2 OC. V1118 O D. VILLE
1. Evaluate the complex integral: ∫C [zRe(z) − z¯Im(z)]dz, where C is the line segment joining...
1. Evaluate the complex integral: ∫C [zRe(z) − z¯Im(z)]dz, where C is the line segment joining −1 to i. (z¯ = z bar) 2. Evaluate the complex integral: ∫ C [iz^2 − z − 3i]dz, where C is the quarter circle with centre the origin which joins −1 to i.
1. Evaluate the line integral S3x2yz ds, C: x = t, y = t?, z =...
1. Evaluate the line integral S3x2yz ds, C: x = t, y = t?, z = t3,0 st 51. 2. Evaluate the line integral Scyz dx - xz dy + xy dz , C: x = e', y = e3t, z = e-4,0 st 51. 3. Evaluate SF. dr if F(x,y) = x?i + xyj and r(t) = 2 costi + 2 sin tj, 0 st St. 4. Determine whether F(x,y) = xi + yj is a conservative vector field....
2. Evaluate a. [sin z,d/dz] b. [d2/dx,ax2 + bx + c] where a, b, and c...
2. Evaluate a. [sin z,d/dz] b. [d2/dx,ax2 + bx + c] where a, b, and c are const. c. [d/dx , da/dx2]
1. (2 points) Find F dF if curl(F) 3 in the region defined by the 4 curves and C4 Ci F . d7 where F(x,y,z)-Wi +pz? + Vi> and C consists of the arc of the 2. (2 points) Evaluate curve y = sin(...
1. (2 points) Find F dF if curl(F) 3 in the region defined by the 4 curves and C4 Ci F . d7 where F(x,y,z)-Wi +pz? + Vi> and C consists of the arc of the 2. (2 points) Evaluate curve y = sin(x) from (0,0) to (π, 0) and the line segment from (π,0) to (0,0). 4 3 3. (2 points) Evaluate F di where F.y,(ry, 2:,3) and C is the curve of intersection of 5 and y29. going...
(1 point) х Suppose w 9 y + where у 2 + sin(2t), and z =...
(1 point) х Suppose w 9 y + where у 2 + sin(2t), and z = z X = e e5t, y 2 + cos(7t). as X. dw A) Use the chain rule to find as a function of x, y, z, and t. Do not rewrite x, y, and z in terms of t, and do not rewrite e e5t d dw 5/y(e^5t)+-x/y^2+1/z(2cos(2t))+(-y/3^2)*(-7sin(7t)) dt Note: You may want to use exp() for the exponential function. Your answer should be...
Problem 1 (10). Let C denote the circle 2| = 2 in the positive direction. Evaluate...
Problem 1 (10). Let C denote the circle 2| = 2 in the positive direction. Evaluate the integrals. 4.50 (a) (2-3 2ds C (2) ee2 (b) peli-2)
Problem 1 (10). Let C denote the circle 2| = 2 in the positive direction. Evaluate the integrals. 4.50 (a) (2-3 2ds C (2) ee2 (b) peli-2)
Q5) Evaluate $c f(z) dz where C is the unit circle Iz| = 1 and f(2) is defined as follows a) f(z) = z2+z2+z_ b) f(x) = tan z c) f() = cosha
1. Evaluate the integral of f(r, θ, φ)-1 + r2 cos2( over a sphere of radius h. (Hint: we did most of this problem in class; 9) sin φ
1. Evaluate the integral of f(r, θ, φ)-1 + r2 cos2( over a sphere of radius h. (Hint: we did most of this problem in class; 9) sin φ
Evaluate Sc (2+2)dy where C is described by parametric equations x(t) = cos(t), y= sin(t), z = 2,0 <t< Select one: O A. +2 O B. 1+2 O C.-1 OD. -1 ABC is a triangle in R where A =(1,4,5), B =(2,-1,0) and C =(4, 2, -3). Find the area of ABC. Select one: O A. (-30,7, -13) O B. -2 OC. V1118 O D. VILLE
1. Evaluate the line integral S3x2yz ds, C: x = t, y = t?, z = t3,0 st 51. 2. Evaluate the line integral Scyz dx - xz dy + xy dz , C: x = e', y = e3t, z = e-4,0 st 51. 3. Evaluate SF. dr if F(x,y) = x?i + xyj and r(t) = 2 costi + 2 sin tj, 0 st St. 4. Determine whether F(x,y) = xi + yj is a conservative vector field....
2. Evaluate a. [sin z,d/dz] b. [d2/dx,ax2 + bx + c] where a, b, and c are const. c. [d/dx , da/dx2]
1. (2 points) Find F dF if curl(F) 3 in the region defined by the 4 curves and C4 Ci F . d7 where F(x,y,z)-Wi +pz? + Vi> and C consists of the arc of the 2. (2 points) Evaluate curve y = sin(x) from (0,0) to (π, 0) and the line segment from (π,0) to (0,0). 4 3 3. (2 points) Evaluate F di where F.y,(ry, 2:,3) and C is the curve of intersection of 5 and y29. going...
(1 point) х Suppose w 9 y + where у 2 + sin(2t), and z = z X = e e5t, y 2 + cos(7t). as X. dw A) Use the chain rule to find as a function of x, y, z, and t. Do not rewrite x, y, and z in terms of t, and do not rewrite e e5t d dw 5/y(e^5t)+-x/y^2+1/z(2cos(2t))+(-y/3^2)*(-7sin(7t)) dt Note: You may want to use exp() for the exponential function. Your answer should be...
Problem 1 (10). Let C denote the circle 2| = 2 in the positive direction. Evaluate the integrals. 4.50 (a) (2-3 2ds C (2) ee2 (b) peli-2)
Problem 1 (10). Let C denote the circle 2| = 2 in the positive direction. Evaluate the integrals. 4.50 (a) (2-3 2ds C (2) ee2 (b) peli-2)
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