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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 φ (x,y) = 2x + y ?. 1 2 3. 1. 2. 3. None of the above.

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

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  1. 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

  2. Which of the following contour plots best represents φ(x,y) = 2x + y ? 1 2 3 1. 2. 3. 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.

  4. Which of the following diagrams represents the unit vectors i and j? 1 2 3 4 3. 4. 1. 2.

  5. φ(x,y,z)= xy - x²yz² + y²zFind gradφ xyi - x²yz²j + y²zk yi - x²z²j – 2x²y²zk (y – 2yz²)i + (x - x²z² + 2z)j+ y²k (y – 2xyz²)i + (x - x²z² + 2yz)j+ (y²-2x²yz)k

  6. φ = 3x + 2xy²z - y²z²Find gradφ (3+2y²z)i + (2x–z)2yzj +(x–z)2y²k (3+2y²z)xi + (2x–z)2y²zj +(x–z)2y²zk 3i + 4xyzj – 2y²zk 3i + 4xyzj + 2y²zk

  7. gradf can also be written as which of the following? 1 2 3 4 1. 2. 3. 4.

  8. Which of the following shows positive divergence? 1 2 3 1. 2. 3.

  9. F = xi +xyj – xyzkFind divF 1 + x – xy i + xj – xyk x + y – xy x + xy – xyz

  10. v = axyi – ½y²j – yzkFind div v (a + 2)y (a – 2)y (2 – a)y a – 2y

  11. Using div v = (a – 2)y, find a to ensure fluid is incompressible 0 1 2 3

  12. F = xi + xyj – xyzkFind 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

  13. F = 3yzi – xzj + 2xy²zkFind 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

  14. 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

  15. 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

  16. A = xyzi + xy²j - x²zk and φ = 3xyz²Find ( )φ 3xyz²(yzi + xyj – 2x²k) 3xyz²(yz + xy – 2x²) 3xyz²(yzi + 2xyj – x²k) 3xyz²(yz + 2xy – x²)

  17. φ = 2xy²z³ - x²z² +yz. Find z(z + 4xz² +12xy²) z²i + 4xz³j + 12xy²zk z²(2y + x + 4xyz + 6xy²z) -2z² + 4xz³ + 12xy² - 2x²

  18. If φ = x²y³z³. Find the rate of change of φ at (1,3,1) in the direction of 1 2 3 4 1. 2. 3. 4.

  19. Given 2 3 4 Don’t Know Find where C is the closed path shown on the diagram below

  20. r = 3ti + (8t – 2t²)j. Find 7t 3ti + 4tj 11 – 4t 3i + (8 – 4t)j

  21. A magnetic field B is given by. Find 1 2 3 4 1. 2. 3. 4.

  22. Given 1 2 3 What is divF ? 1. 2. 3.

  23. Find 1 2 3 4 1. 2. 3. 4.

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