Calculus 3 :

final answers only are okay please highlight the final result !

Section 12.1: Problem 1 (1 point) Consider the solid that lies above the square (in the xy-plane) R = [0, 2] x [0, 2]. and below the elliptic paraboloid z = 25 - x2 - 2y?. (A) Estimate the volume by dividing R into 4 equal squares and choosing the sample points to lie in the lower left hand corners. (B) Estimate the volume by dividing R into 4 equal squares and choosing the sample points to lie in the upper right hand corners. (C) What is the average of the two answers from (A) and (B)?Section 12.1: Problem 10 {1 point} Find the average value of 319:, y] 2 Be" a: + all over the rectangle R = [l], 5] x [[1,6]. Average value = E] Section 12.1: Problem 11 {1 point} The table below gives values of f(z, y), the number of milligrams of mosquito larvae per square meter in a swamp. lie and y are in meters and R is the rectangle [J g a: E 6, t] g y g 12, estimate Hit-n\": y)dA. z, y]dA m D {include traits in your answer.) Hint: Evaluate the Riemann sums using the lower lelt comers and upper right comers. Then take the average of the two Riemann sums. Section 12.1: Problem 12 (1 point) Calculate a Riemann sum $3,3 on the square R = [0, 3] x [0, 3] for the function g(x, y) = f(x, y) + 9. The contour plot of f(c, y) is shown in Figure 4. Choose sample points and use the plot to find the values of f(x, y) at these points. Use the values of f(x, y) to evaluate g(r, y) accordingly. 2- 32 P X 0 FIGURE 4 Contour plot of f(x, y). $3,3 =Section 12.1: Problem 2 {1 point} Using geometry, calculate the volume of the solid under 2 = 1.! 15 z? y? and over the circular disk 9:2 + y2 <_i d section problem point evaluate the iterated integral jo dady calculate double ffr i cos y da where r is region: cy5 consider solid that lies above square xvplane x and below elliptic paraboloid z="49" a:2 using integrals compute exact value of volume. c>