Suppose X Hypergeometric (N, b, n). Show that if N, b, n approach in a way such that →p and Nb → 1 – p, then P(X = k) → (")p² (1 − p)”→k.
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- Sketch the cylinder given by x = 4- Z*2（z square）in three-dimensional space.Evaluate the triple integral ∭ExydV where E is the solid tetrahedon with vertices (0,0,0),(2,0,0),(0,6,0),(0,0,4)Find the appropriate parametrization for the given piecewise smooth-curvein R^2, with the implied orientation. The curve C, which goes along the circle of radius 3, from the point(3,0) above the x-axis to the point (-3,0), and then in a straight line along the x-axis back to (3,0).
- Find the points on the surface xy2z3=2 that are closest to theorigin.Suppose that the Celsius temperature at the point (x, y, z) on the sphere x2 + y2 + z2 = 1 is T = 400xyz2. Locate the highest and lowest temperatures on the sphere.Suppose that a thin metal plate of area A and constant density doccupies a region R in the xy-plane, and let My be the plate’s momentabout the y-axis. Show that the plate’s moment about the linex = b is My - bδA if the plate lies to the right of the line, and
- Compute c and d without using divergence theoremShow that the intrinsic equations of a helix on a cone of revolution are : K= 1/as and torsion=1/bs where a,b are constant step by step with all detHow 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 ? Any help would be greatly appreciated. :)
