Homework Answers
1. An iterated double integral that is equivalent to *** dx + ry dy JOR 3....
1. An iterated double integral that is equivalent to *** dx + ry dy JOR 3. Use Groen's Theorem to set up an iterated double integral equal to the line integral $+eva) dx +(2+ + cow y) dy where is the boundary of the region enclosed by the parabolas y rand 1 = y2 with positive orientation. This yields: A. where R is the triangular region with vertices (0,0),(1,0) and (0,1) is: A B. B. So ['(2-z) dr de SL...
R R 5. To compute 1 = lim 2 COS dr and J = lim 22+1...
R R 5. To compute 1 = lim 2 COS dr and J = lim 22+1 sinc dx simultaneously .22 +1 R R0 R R using Residue Theorem, let f(x) 22 +1 C COSC sinc (1) Show that if z = x + iy, then Rf(R2) = and Sf(R2) = x2 +1 x2 +1 (2) Find Res[f, i]. (3) Show that I = 0 and J (4) Prove I = 0) in the above problem without using Residue Theorem. IT
C. This problem is about the inhomogeneous equation dy (1-)2 (1+ x) dy (1-3) (I) y=re...
C. This problem is about the inhomogeneous equation dy (1-)2 (1+ x) dy (1-3) (I) y=re +x dr dr2 and the corresponding homogeneous equation dy dy +x dr2 (1- r) (H) -y 0. dr (i) Show that y=r and y= e are solutions of (H). (ii) From (), the general solution of (H) must be y= Ar + Be for arbitrary constants A and B. Solve (I) by the variation of parameters method of Lesson 22, i.e., setting y ur...
Q2(a) Find the following derivative of function f(x,y) 0 at point (2, 3). (i) dr dy...
Q2(a) Find the following derivative of function f(x,y) 0 at point (2, 3). (i) dr dy (2 marks) (ii) dr dx (2 marks) (iii) dxdy (4 marks) (b) Suppose that the volume of water in a tank for time range 0 st 56 is given by function 20) = 10 +51 - (i) Describe, is the volume of water increasing or decreasing at : = 0? (2 marks) (1) Describe, is the volume of water increasing or decreasing at =...
2 + COS- 2.ry dy d 1+y2 = y(y + sin x), 7(0) = 1. 3....
2 + COS- 2.ry dy d 1+y2 = y(y + sin x), 7(0) = 1. 3. [2cy cos(x+y) - sin x) dx + x2 cos (+²y) dy = 0. 4. Determine the values of the constants r and s such that (x,y) = x'y is an Integrating Factor for the following DE. (2y + 4x^y)dr + (4.6y +32)dy = 0. 2. C = -1 You need to find the solution in implicit form. 3. y = arcsin (C-cos) 4. r=...
(a) Use the figure to find the value of srca f(r) dr. -3 Y 2 f(r)...
(a) Use the figure to find the value of srca f(r) dr. -3 Y 2 f(r) -2 -1 2 3 4 -2 f(x) dx (b) If the area of the shaded region is A, what is f(x) dx? Lore f(x) dx %3D
Problem #3 Solve initial value problem as follows: 1 r2 dạy dy + 4x dx2 dx...
Problem #3 Solve initial value problem as follows: 1 r2 dạy dy + 4x dx2 dx + 2 y = y|x=1 dy dx = 2, | x=1 = 3. х dy Calculate the value of at the point where x = 2, round-off your value of the derivative to four figures and dx present your result below (10 points): (your numerical result for the derivative must be written here)
work step by step. Thanks الم 3. Let k : (0,1] x [0, 1] + R...
work step by step. Thanks
الم 3. Let k : (0,1] x [0, 1] + R be a continuous function and let f be a Lebesgue integrable function on (0,1). (a) Show that for each y € (0,1), 2 + f(-x){}(2", y) is Lebesgue integrable on (0,1). (b) Define g : [0, 1] +R by 8(u) = Sam Slam)x(x, y)dır. 10,11 Prove that g is continuous at cach y € (0, 1].
(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...
(1 point) Suppose y = 7x In r. Find the differential: dy = dr. We were...
(1 point) Suppose y = 7x In r. Find the differential: dy = dr. We were unable to transcribe this image(1 point) Consider the function f(x) = –2r3 +33x2 – 144x + 2. (a) Find all critical numbers c off. C= (b) f is increasing for re (c) f is decreasing for se Note: Input U, infinity, and -infinity for union, o, and -o, respectively. If there are multiple answers, separate them by commas. If there is no answer, input...
1. An iterated double integral that is equivalent to *** dx + ry dy JOR 3. Use Groen's Theorem to set up an iterated double integral equal to the line integral $+eva) dx +(2+ + cow y) dy where is the boundary of the region enclosed by the parabolas y rand 1 = y2 with positive orientation. This yields: A. where R is the triangular region with vertices (0,0),(1,0) and (0,1) is: A B. B. So ['(2-z) dr de SL...
R R 5. To compute 1 = lim 2 COS dr and J = lim 22+1 sinc dx simultaneously .22 +1 R R0 R R using Residue Theorem, let f(x) 22 +1 C COSC sinc (1) Show that if z = x + iy, then Rf(R2) = and Sf(R2) = x2 +1 x2 +1 (2) Find Res[f, i]. (3) Show that I = 0 and J (4) Prove I = 0) in the above problem without using Residue Theorem. IT
C. This problem is about the inhomogeneous equation dy (1-)2 (1+ x) dy (1-3) (I) y=re +x dr dr2 and the corresponding homogeneous equation dy dy +x dr2 (1- r) (H) -y 0. dr (i) Show that y=r and y= e are solutions of (H). (ii) From (), the general solution of (H) must be y= Ar + Be for arbitrary constants A and B. Solve (I) by the variation of parameters method of Lesson 22, i.e., setting y ur...
Q2(a) Find the following derivative of function f(x,y) 0 at point (2, 3). (i) dr dy (2 marks) (ii) dr dx (2 marks) (iii) dxdy (4 marks) (b) Suppose that the volume of water in a tank for time range 0 st 56 is given by function 20) = 10 +51 - (i) Describe, is the volume of water increasing or decreasing at : = 0? (2 marks) (1) Describe, is the volume of water increasing or decreasing at =...
2 + COS- 2.ry dy d 1+y2 = y(y + sin x), 7(0) = 1. 3. [2cy cos(x+y) - sin x) dx + x2 cos (+²y) dy = 0. 4. Determine the values of the constants r and s such that (x,y) = x'y is an Integrating Factor for the following DE. (2y + 4x^y)dr + (4.6y +32)dy = 0. 2. C = -1 You need to find the solution in implicit form. 3. y = arcsin (C-cos) 4. r=...
(a) Use the figure to find the value of srca f(r) dr. -3 Y 2 f(r) -2 -1 2 3 4 -2 f(x) dx (b) If the area of the shaded region is A, what is f(x) dx? Lore f(x) dx %3D
Problem #3 Solve initial value problem as follows: 1 r2 dạy dy + 4x dx2 dx + 2 y = y|x=1 dy dx = 2, | x=1 = 3. х dy Calculate the value of at the point where x = 2, round-off your value of the derivative to four figures and dx present your result below (10 points): (your numerical result for the derivative must be written here)
work step by step. Thanks
الم 3. Let k : (0,1] x [0, 1] + R be a continuous function and let f be a Lebesgue integrable function on (0,1). (a) Show that for each y € (0,1), 2 + f(-x){}(2", y) is Lebesgue integrable on (0,1). (b) Define g : [0, 1] +R by 8(u) = Sam Slam)x(x, y)dır. 10,11 Prove that g is continuous at cach y € (0, 1].
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...
(1 point) Suppose y = 7x In r. Find the differential: dy = dr. We were unable to transcribe this image(1 point) Consider the function f(x) = –2r3 +33x2 – 144x + 2. (a) Find all critical numbers c off. C= (b) f is increasing for re (c) f is decreasing for se Note: Input U, infinity, and -infinity for union, o, and -o, respectively. If there are multiple answers, separate them by commas. If there is no answer, input...
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