Reference no: EM131073194
1. If w = f(x, y, z), where x = x(t, u), y = y (t, u), and z = z (t, u), use the chain rule to write out expression for ft and fu.
2. Find the maximum directional derivates and the direction in which it occurs for f(x, y) = 3x2 + siny at the point (1, 0).
3. Find the classify the local extrema of f(x, y) = x4 + y4 - 4xy.
4. Find the points on the surface z2 = xy + 1 that are closest to the origin.
5. Calculate the exact value of -1∫1x2∫1(x+2y)dA.
6. Sketch the region of integration and change the order of integration for 0∫40∫√xf(x, y) dy dx.
7. Find the volume under the paraboloid z = x2 + y2 and above the disk x2 + y2 ≤ 1.
8. Set up, but do not evaluate the integrals required to compute the centre of mass for the region bounded by x = 0, x = 1, y = 0 and y = x2 if density is proportional to distance from the x-axis.
9. Find the area of the portion of the surface z = x + y2 that lies above a triangle with vertices (0, 0), (1, 1), and (0, 1).
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What potential legal or ethical issues could arise
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Find the area of the portion of the surface
: Find the volume under the paraboloid z = x2 + y2 and above the disk x2 + y2 ≤ 1. Find the area of the portion of the surface z = x + y2 that lies above a triangle with vertices (0, 0), (1, 1), and (0, 1)
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Prove the theorems given below
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Does the equation ax = 0 have a nontrivial solution
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