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- Consider the unit cirlce in the plane; that is, the set of all points within a distanceof 1 of the origin: A= {(x, y) : x^2 + y^2 ≤ 1}.Suppose we choose a point (X, Y ) uniformly at random from S. What is the pdf for thedistance B = √X^2 + Y ^2 from the origin to this point? Hint given: What is the cdf of B?Evaluate the divergence of F = (exy, xy, z4) at P = (l, 0, 2).Compute the divergence of the function v (provided in the attatched image). Check the divergence theorem for this function, using as your volume the inverted hemispherical bowl of radius R, resting on the xy plane and centered at the origin (See attached image of Fig. 1.40).
- If c is a line segment from z=2 to z=2i, prove without finding the value of the integralSuppose X has the B(20, 0.5) distrubution. Using normal approximation for X with the continuity correction calculate the P(x < 6)Evaluate the given integral where C is the directed line segment that joins the point 1 to the point 3+4i.
- Every E Jordan that is an undirected piecewise smooth curve of the topological n r clock for the region Area(E) = 1 2nd Z ∂E xdy - ydx show that.Calculate the integral below approximately using the n=2 Gauss quadrature methodSuppose X has the B(20, 0.5) distrubution. Using normal approximation for X with the continuity correction calculate the P(x ≤ 10)