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Which of the following contour plots best represents φ(x,y) = 2x + y ? 1. 1 2 3 2. None of the above 3.

### Transcript of What are the contours of f(x,y) = x-3y?

What are the contours of f(x,y) = x-3y?
Straight lines of gradient -3 Straight lines of gradient 3 Straight lines of gradient -1/3 Straight lines of gradient 1/3 Which of the following contour plots best represents (x,y) = 2x + y ?
1. 1 2 3 2. None of the above 3. If C is a closed contour, what symbol is used when evaluating a line integral?
1 2 3 4 1. 2. 3. 4. Which of the following diagrams represents the unit vectors i and j?
1 2 3 4 1. 2. 3. 4. (x,y,z)= xy - xyz + yz Find grad
xyi - xyzj + yzk yi - xzj 2xyzk (y 2yz)i + (x - xz + 2z)j+ yk (y 2xyz)i + (x - xz + 2yz)j+ (y-2xyz)k = 3x + 2xyz - yz Find grad
(3+2yz)i + (2xz)2yzj +(xz)2yk (3+2yz)xi + (2xz)2yzj +(xz)2yzk 3i + 4xyzj 2yzk 3i + 4xyzj + 2yzk gradf can also be written as which of the following?
1 2 3 4 1. 2. 3. 4. Which of the following shows positive divergence?
1. 1 2 3 2. 3. F = xi +xyj xyzk Find divF
1 + x xy i + xj xyk x + y xy x + xy xyz v = axyi yj yzk Find div v
(a + 2)y (a 2)y (2 a)y a 2y Using div v = (a 2)y, find a to ensure fluid is incompressible
1 2 3 F = xi + xyj xyzk Find curlF
(-z-y)xyi + (yz+1)xj +(y-1)xk (-z-y)xyi - (yz+1)xj +(y-1)xk -xzi yzj + yk - xzi + yzj + yk F = 3yzi xzj + 2xyzk Find curlF
(4yz+1)xi + (2yz-3)yj - 4zk (4yz+1)xi - (2yz-3)yj - 4zk -2zi + (4yz+1)xj + (3-2yz)yk -2zi (4yz+1)xj + (3-2yz)yk The curl of a vector field measures which of the following?
The greatest rate of change at any point The rate at which fluid is flowing away from a point The rotation at a point Which of the following statements are true?
div(grad f) exists and is a scalar grad(div v) exists and is a scalar div(curl v) exists and is a vector curl(div v) exists and is a vector A = xyzi + xyj - xzk and = 3xyz Find ( )
3xyz(yzi + xyj 2xk) 3xyz(yz + xy 2x) 3xyz(yzi + 2xyj xk) 3xyz(yz + 2xy x) = 2xyz - xz +yz. Find z(z + 4xz +12xy) zi + 4xzj + 12xyzk
z(2y + x + 4xyz + 6xyz) -2z + 4xz + 12xy - 2x If = xyz. Find the rate of change of at (1,3,1) in the direction of
2 3 4 1. 2. 3. 4. Find where C is the closed path shown on the diagram below
Given Find where C is the closed path shown on the diagram below 2 3 4 Dont Know r = 3ti + (8t 2t)j. Find 7t 3ti + 4tj 11 4t 3i + (8 4t)j A magnetic field B is given by. Find
1 2 3 4 1. 2. 3. 4. Given What is divF ? 1. 1 2 3 2. 3. Find 1. 1 2 3 4 2. 3. 4.