TRANSCRIBE THE FOLLOWING TEXT IN DIGITAL FORMAT
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TRANSCRIBE THE FOLLOWING TEXT IN DIGITAL FORMAT
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- How would I solve ∭xzdV, where E is bounded by the planes z = 0, z=y, and the cylinder x2 + y2 = 1 in the half-space y ≥ 0 ? Thanks for you help in advance. :)A company has $300,000 to spend on two products. Suppose that theUtility derived by the company from x units of the first product and yunits of the second product is given byU(x,y) = 5000x0.75y0.25(i) Show that U is homogenous to some degree. (ii) Show that Euler’s Theorem holds for the function U(x,y)How would I go about solving ∭xzdV, where E is bounded by the planes z = 0, z=y, and the cylinder x2 + y2 = 1 in the half-space y ≥ 0 ? Thanks for you help. :)
- A company has $300,000 to spend on two products. Suppose that the Utility derived by the company from x units of the first product and y units of the second product is given by U(x,y) = 3000x0.65y0.35 (i) Show that U is homogenous to some degree . (ii) Show that Euler’s Theorem holds for the function U(x,y)Bounded by the cylinder x 2 + y 2 = 1 and the planes y= z x =0 z= 0 in the first octantAll students are located at integral coordinates in the xy-plane. The x-coordinates belong to the set {-2, -1, 0, 1, 2}, and the y-coordinates belong to the set {-1, 0, 1, 2, 3}. Abel is seated on the line which is normal to the curve f(x) = x2 – 2x + 4 at the point (1, 3). The curve y =ax2 +bx +c passes through the point (2, 4) and is tangent to the line y = x + 1 at (0, 1). Determine values for a, b, and c. Gauss sits at the point (-b –c, 4a). Jacobi is seated on the line tangent to the graph of y =2x3 -3x2 -12x +21 at x =2.
- Show that limit t appraoaches infinity integral -t to t x dx =0 This shows that we can’t define integral - infinity to infinity f(x) dx = limit t appraoaches infinity integral -t to t f(x) dx1.Suppose that f : [0, 1] −→ [0, 1] is a continuous function. Prove that f has afixed point in [0, 1], i.e., there is at least one real number x ∈ [0, 1] such thatf(x) = x. 2.The axes of two right circular cylinders of radius a intersect at a right angle.Find the volume of the solid of intersection of the cylinders.I found a textbook example which intergrates an area function to find the volume of a solid of revolution bounded by the curve f(x) = (x-1)2 about the x-axis and the lines x=0 and x=2 using the disk method. The example shows a final solution change of intergration interval to x=1 and x=3 to arrive at the answer of 242pi/3 instead of the original interval x=0 and x=2? Would you show me step-wise how this was done or why it was necessary?