Number 7 Please Find the minimum and maximum values of the function subject to t

Question

Number 7 Please

Find the minimum and maximum values of the function subject to the constraint. F(x. y, z) = 3x + 2y + 4z, x^2 + 2y^2 + = 1 Compute the Riemann sum S for the double integral where R = [1, 4] x [1, 3], for the grid and sample points shown in figure below. The following table gives the approximate height (in meters) at quarter-meter intervals of a mound of gravel. Estimate the volume V of the mound by computing the average of the two Riemann sums_4,3 with lower-left and upper-right vertices of the sub rectangles as sample points. V= m^3

Explanation / Answer

Sum = Double integral from x=1 to 4 from y= 1 to 3 (10x+9y)dydx

Sum =from x=1 to 4 from y= 1 to 3 (5x^2y+(9/2)xy^2)

Sum = (5(16-1)(3-1)+(9/2)(4-1)(9-1))

Sum= 150+108=258

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