Differentiability of Foxy) at point (d,6) Let f:R R be a Funetion given by xy x-y = Fory) if (y) +(0,0) iF (IY) = (0,0)
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- Maximum divergence Within the cube {(x, y, z): | x | ≤ 1, | y | ≤ 1, | z | ≤ 1}, where does div F have the greatest magnitude when F = ⟨x2 - y2, xy2 z, 2xz⟩?A space curve Let w = x2e2y cos 3z. Find the value of dw/ dt at the point (1, ln 2, 0) on the curve x = cos t, y = ln (t + 2), z = t.StokesTheorem.Evaluate∫ F·dr,whereF=arctanx/yi+ln√x2+y2j+k and C is the boundary of the triangle with vertices (0, 0, 0), (1, 1, 1), and (0, 0, 2).
- 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)Determine if f (x, y) = ={(xsin3y)/(x2+y6), (x, y) ≠ (0, 0) ={1, (x, y) = (0, 0) is continuous at (0, 0)Divergence theorem for F = 3 i + xy j + x k. Taken over a region bounded by z = 4 - y2, x = 0, x = 3, and the xy-plane.
- Use Stokes's Theorem to evaluate F · dr C . In this case, C is oriented counterclockwise as viewed from above. F(x, y, z) = 2yi + 3zj + xk C: triangle with vertices (5, 0, 0), (0, 5, 0), (0, 0, 5)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)All 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.