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Q1) Sketch the following vector fields, showing vector at whole number coordinates be- tween -2 a...
please answer asap (it is all the professor asked)
(5) Consider the gradient vector field F ▽f where f(x,y) = cos(2x-3y). Find curves G and C2 that are not closed such that JG F·dr = 0 and 1, F . dr-1. Explain why you pick the curve you do, and how you know the integrals have the correct values. (Hint: Try picking a straight line between the origin and some simple point (a, b) that you choose later.)
(5) Consider...
Problem 6. Consider the system: y. and its corresponding vector field: 1. Sketch a number of different solution curves on the phase plane. 2. Describe the behavior of the solution that satisfies the initial condition (to, o) (0, 2)
Problem 6. Consider the system: y. and its corresponding vector field: 1. Sketch a number of different solution curves on the phase plane. 2. Describe the behavior of the solution that satisfies the initial condition (to, o) (0, 2)
answer all parts please except A if you cannot
(6) Consider the vector field F(x,y)-《22, 3y). A path is closed if it ends whiere it starts Consider the 3 closed paths starting and ending at (3,0): C1 the circle of radius 3 centered at the origin, C2 the ellipse with equation 2 +3y2-9, and Cs the flat linear path going to -3 and then going straight back. (a) Use GeoGebra to plot the vector field F (b) For each, parametrize...
1. (1.5 points) Sketch the following vector fields: (B) B(x,y)=(z-y,2). (C) Vf where f(x,y) = xy
1. (1.5 points) Sketch the following vector fields: (B) B(x,y)=(z-y,2). (C) Vf where f(x,y) = xy
A. Make a sketch of a vector F- (x,y, z), labeling the appropriate spherical coordinates. In addition, show the unit vectors r, θ, and φ at that point B. Write the vectors ŕ.0, and ф in terms of the unit vectors x, y, and г. Here's the easy way to do this 1. For r, simply use the fact that/r 2. For φ, use the following formula sin θ Explain why the above formula works 3. Compute θ via θ...
1. (This is problem 5 from the second assignment sheet, reprinted here.) Consider the nonlinear system a. Sketch the ulllines and indicate in your sketch the direction of the vector field in each of the regions b. Linearize the system around the equilibrium point, and use your result to classify the type of the c. Use the information from parts a and b to sketch the phase portrait of the system. 2. Sketch the phase portraits for the following systems...
True or False Determine whet her the statement is true or false, and circle the correct answer. Each question is worth 2 points. (1) If F is a vector field and C is an oriented curve, then F dr must be less than zero. F (2) It is possible that for a certain vector field F and piecewise smooth oriented path C we have/. F. dr-2i-Sj. (3) Suppose d·is the unit square joining the points (0,0), (1,0), (1,1), (0.1) oriented...
Please help with 3 and 4.
518 Guided Projects Guided Project 77: Planimeters and vector fields Topics and skills: Vector calculus, Stokes' Theorem The planimeter is an ingenious device that allows one to trace a closed curve in the plane and determine the area of the region R enclosed by the curve (Figure 1). For this reason, it is an example of an "integrator," a mechanical device that computes areas of regions bounded by curves. The original planimeter was invented...
please help ! Q1-Q6
1. Let F (3x - 4y +22)i+(4x +2y 3z2)j + (2xz moving once around an 4y zk be a vector field. Consider a particle ellipse C given by parametrization r= 4 cos ti +3 sin tj. Find the work done. 3 3 = 3, y=-- and 2 1 2. Let D be the region in the first quadrant bounded by the lines y=-r1, y 4 + 1. Use the transformation u 3 2y, v r +...
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NAME Q1. (30pts) Solve the quadratic equation z2-(3+3i)z +6+2i = 0 by realizing the following plan: (i) find the discriminant A of the equation; (ii) write a program for a scientific calculator to obtain the polar form r(cos 0 + i sin 0) of A and the 'first' root + isin COS 2 of degree two of A; (iii) execute the program, fix the results, find another root A2 of A of degree two (before executing the program,...