Evaluate using integration by parts.


Mathematics

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Find the average rate of change of the function over the given interval.  y = , [2, 8]

A. 2
B. 7
C. - 
D.

Mathematics

Find fx, fy, and fz.f(x, y, z) = z(ex)y

A. fx = zyexy; fy = zxexy; fz = zexy  B. fx = zyexy; fy = zxexy; fz = exy  C. fx = zexy; fy = zexy; fz = exy  D. fx = zxexy; fy = zyexy; fz = exy 

Mathematics

Provide an appropriate response.Explain why the following four statements ask for the same information.(i) Find the roots of f(x) = 3x3 - 3x - 1(ii) Find the x-coordinates of the intersections of the curve y = x3 with the line y = 3x + 1.(iii) Find the x-coordinates of the points where the curve y = x3 - 3x crosses the horizontal line .(iv) Find the values of x where the derivative of g(x) = x4 - x2 - x + 5 equals zero.

What will be an ideal response?

Mathematics

You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft3.)

Mathematics