Evaluate using integration by parts.
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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.
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
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?
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.)