![6. Plot the 3D surface and contour levels of the following function: z(x, y)cos(2y-x) sin(2x) such that-π x π and-r y < π [10 marks] 7. Create a 5 x 5 random matrix M6 with elements ranging from 10 to 33. Using indexing, define the following arrays: An array containing all elements of M6 that are greater than 3 and smaller 6 marks] An array containing all elements of M6 that are negative or between 29 and 33. 6 marks a. than 25; b.](http://img.homeworklib.com/questions/ee9b58d0-8c05-11eb-b6e8-c55ba09face6.png?x-oss-process=image/resize,w_560)
Homework Answers
We can plot the 3-D surface and the contour levels of this function using Mathematica.
Post the second question separately. Please comment if you have any queries. Thanks!
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6. Plot the 3D surface and contour levels of the following function: z(x, y)cos(2y-x) sin(2x) such...
Create a surface plot and a contour plot of the function z=(x-2)^2+2xy+y^2. Using the matlab
Create a surface plot and a contour plot of the function z=(x-2)^2+2xy+y^2. Using the matlab
Problem 2: Create a surface plot and a contour plot of the function f(x, y) =...
Problem 2: Create a surface plot and a contour plot of the function f(x, y) = xe-I(x-y2)*+y?] Where -2 x 2 and -2 < y s 2. Use a step size of 0.1. Add labels to the axis
Problem 2: Create a surface plot and a contour plot of the function f(x, y) = xe-I(x-y2)*+y?] Where -2 x 2 and -2
5. 2 cos x cos y= cos(x+y) + cos (x-y) 6. sin2x + sin 2y =...
5. 2 cos x cos y= cos(x+y) + cos (x-y) 6. sin2x + sin 2y = 2 sin(x+y)cos(x-y)
I. For the function. /(x) -X-4X+2XY+2Y+2Y+14 a. Plot the surface function for X over [5 6]. and Y...
Please use matlab for the following problem
I. For the function. /(x) -X-4X+2XY+2Y+2Y+14 a. Plot the surface function for X over [5 6]. and Y over [-4, -2]. ecolour plot for X over [O 101 and Yover [43] and values for the contours of V [1 1.25 1.5 22.5 3] c. Write an m-file to find the minimum of the function using the gradient descent method Use a starting value of [4, -4].
I. For the function. /(x) -X-4X+2XY+2Y+2Y+14 a....
1). For the function, f(x) X-4X+2XY+2Y2+2Y+14 a. Plot the surface function for X over [5 61, and ...
1). For the function, f(x) X-4X+2XY+2Y2+2Y+14 a. Plot the surface function for X over [5 61, and Y over [-4,-2]," b. Draw the contour plot for X over [0 10], and Y over [-4,-2] and values for the contours 1.25 1.5 2 25 3 of V c. Write an m-file to find the minimum of the function using the gradient descent method. Use a starting value of [4,-4].
1). For the function, f(x) X-4X+2XY+2Y2+2Y+14 a. Plot the surface function for...
Question 4 (2+4+4+1+4 = 15 marks) Consider the function y = 4 sin (2x-π) for-r below to sketch the graph of y. x < π. Follow the steps (a) State the amplitude and period in the graph of this funct...
Question 4 (2+4+4+1+4 = 15 marks) Consider the function y = 4 sin (2x-π) for-r below to sketch the graph of y. x < π. Follow the steps (a) State the amplitude and period in the graph of this function 4 sin (22-9 ) for-r (b) Solve y π to find the horizontal intercepts x (a-intercepts) of the function. (c) Find the values of x for-π π for which the maximum. and the x minimum values of the function occur...
3. A shape is defined as: (x, y, z) = (rcos 0 sin 0,r sin sin d, r cos ø) with 0r1, T/4 < 0< 7t/4 and 0 < ¢ &l...
3. A shape is defined as: (x, y, z) = (rcos 0 sin 0,r sin sin d, r cos ø) with 0r1, T/4 < 0< 7t/4 and 0 < ¢ < T* 2 marks (a) Describe this region. an appropriate integration, determine the volume of this shape [4 marks (b) Using 3 (Continued) 3 marks (c) Parametrise the surface of this shape. 3 marks (d) Find a normal to the surface [4 marks (e) What is the surface area of...
2. S is the surface y 2 = 4(x 2 + z 2 ), y ∈ [0, 2] obtained by rotating the function y = 2x about the y-axis for y ∈ [0...
2. S is the surface y 2 = 4(x 2 + z 2 ), y ∈ [0, 2] obtained by rotating the function y = 2x about the y-axis for y ∈ [0, 2]. Find a suitable parametric representation of the surface S using the cylindrical polar coordinates. Answer is: 2. r(u, v) = u cos(v)i + 4uj + u sin(v)k , 0 ≤ v < 2π, 0 ≤ u ≤ 1/2. I am unsure how to work it out...
Let F(x, y, z) = sin yi + (x cos y + cos z)j – ysin...
Let F(x, y, z) = sin yi + (x cos y + cos z)j – ysin zk be a vector field in R3. (a) Verify that F is a conservative vector field. (b) Find a potential function f such that F = Vf. (C) Use the fundamental theorem of line integrals to evaluate ScF. dr along the curve C: r(t) = sin ti + tj + 2tk, 0 < t < A/2.
2. Evaluate the surface integral [[Fids. (a) F(x, y, z) - xi + yj + 2zk,...
2. Evaluate the surface integral [[Fids. (a) F(x, y, z) - xi + yj + 2zk, S is the part of the paraboloid z - x2 + y2, 251 (b) F(x, y, z) = (z, x-z, y), S is the triangle with vertices (1,0,0), (0, 1,0), and (0,0,1), oriented downward (c) F-(y. -x,z), S is the upward helicoid parametrized by r(u, v) = (UCOS v, usin v,V), osus 2, OSVS (Hint: Tu x Ty = (sin v, -cos v, u).)...
Problem 2: Create a surface plot and a contour plot of the function f(x, y) = xe-I(x-y2)*+y?] Where -2 x 2 and -2 < y s 2. Use a step size of 0.1. Add labels to the axis
Problem 2: Create a surface plot and a contour plot of the function f(x, y) = xe-I(x-y2)*+y?] Where -2 x 2 and -2
5. 2 cos x cos y= cos(x+y) + cos (x-y) 6. sin2x + sin 2y = 2 sin(x+y)cos(x-y)
Please use matlab for the following problem
I. For the function. /(x) -X-4X+2XY+2Y+2Y+14 a. Plot the surface function for X over [5 6]. and Y over [-4, -2]. ecolour plot for X over [O 101 and Yover [43] and values for the contours of V [1 1.25 1.5 22.5 3] c. Write an m-file to find the minimum of the function using the gradient descent method Use a starting value of [4, -4].
I. For the function. /(x) -X-4X+2XY+2Y+2Y+14 a....
1). For the function, f(x) X-4X+2XY+2Y2+2Y+14 a. Plot the surface function for X over [5 61, and Y over [-4,-2]," b. Draw the contour plot for X over [0 10], and Y over [-4,-2] and values for the contours 1.25 1.5 2 25 3 of V c. Write an m-file to find the minimum of the function using the gradient descent method. Use a starting value of [4,-4].
1). For the function, f(x) X-4X+2XY+2Y2+2Y+14 a. Plot the surface function for...
Question 4 (2+4+4+1+4 = 15 marks) Consider the function y = 4 sin (2x-π) for-r below to sketch the graph of y. x < π. Follow the steps (a) State the amplitude and period in the graph of this function 4 sin (22-9 ) for-r (b) Solve y π to find the horizontal intercepts x (a-intercepts) of the function. (c) Find the values of x for-π π for which the maximum. and the x minimum values of the function occur...
3. A shape is defined as: (x, y, z) = (rcos 0 sin 0,r sin sin d, r cos ø) with 0r1, T/4 < 0< 7t/4 and 0 < ¢ < T* 2 marks (a) Describe this region. an appropriate integration, determine the volume of this shape [4 marks (b) Using 3 (Continued) 3 marks (c) Parametrise the surface of this shape. 3 marks (d) Find a normal to the surface [4 marks (e) What is the surface area of...
Let F(x, y, z) = sin yi + (x cos y + cos z)j – ysin zk be a vector field in R3. (a) Verify that F is a conservative vector field. (b) Find a potential function f such that F = Vf. (C) Use the fundamental theorem of line integrals to evaluate ScF. dr along the curve C: r(t) = sin ti + tj + 2tk, 0 < t < A/2.
2. Evaluate the surface integral [[Fids. (a) F(x, y, z) - xi + yj + 2zk, S is the part of the paraboloid z - x2 + y2, 251 (b) F(x, y, z) = (z, x-z, y), S is the triangle with vertices (1,0,0), (0, 1,0), and (0,0,1), oriented downward (c) F-(y. -x,z), S is the upward helicoid parametrized by r(u, v) = (UCOS v, usin v,V), osus 2, OSVS (Hint: Tu x Ty = (sin v, -cos v, u).)...
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