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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. - PowerPoint PPT Presentation

### 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 -3Straight lines of gradient 3Straight lines of gradient -1/3 Straight lines of gradient 1/3

• Which of the following contour plots best represents (x,y) = 2x + y ?123

• If C is a closed contour, what symbol is used when evaluating a line integral?1234

• Which of the following diagrams represents the unit vectors i and j? 1234

• (x,y,z)= xy - xyz + yzFind gradxyi - 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 - yzFind 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?1234

• Which of the following shows positive divergence?123

• F = xi +xyj xyzkFind divF1 + x xyi + xj xykx + y xyx + xy xyz

• v = axyi yj yzkFind div v(a + 2)y(a 2)y(2 a)ya 2y

• Using div v = (a 2)y, find a to ensure fluid is incompressible0123

• 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 pointThe rate at which fluid is flowing away from a pointThe rotation at a point

• Which of the following statements are true?div(grad f) exists and is a scalargrad(div v) exists and is a scalardiv(curl v) exists and is a vectorcurl(div v) exists and is a vector

• A = xyzi + xyj - xzk and = 3xyzFind ( )3xyz(yzi + xyj 2xk)3xyz(yz + xy 2x)3xyz(yzi + 2xyj xk)3xyz(yz + 2xy x)

• = 2xyz - xz +yz. Findz(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 of1234

• Given234Dont KnowFind where C is the closed path shown on the diagram below

• r = 3ti + (8t 2t)j. Find 7t3ti + 4tj11 4t3i + (8 4t)j

• A magnetic field B is given by. Find1234

• Given

What is divF ?123

• Find1234