Let f (x, y) = 4 xy n² (n + 1)² is joint pdf with x,y=1,2,3,...,n then V(x/y) is
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- From the partial differential eqiuation by eliminating the arbitrary function z=(x2+y2+z2)Suppose U solves the heat equation on the real lineUt = 4Uxx, x ∈ Rwith initial valueU(x, 0) = (4, x ≤ 02, x > 0.(i) Use the Fourier-Poisson formula to give an explicit expression for the solutionU.(ii) Describe the qualitative behaviour of U in this case as t → ∞ and plot outthe solution at several instants of time to explain your answer. What is the limitof U as t → ∞?Expand x^2y+3y-4 about the point (-1,2) by Taylor's theorem
- . Show that it is possible to solve u and v from:xyu + xy2uv2 = 2 and x2yvu4 + yu3v2 = 2,in terms of x and y uniquely near the point (x, y, u, v) = (1, 1, 1, 1); also find the first four partial derivatives at the point (1, 1).Find the linearization of ƒ(x) = 2x at x = 0. Then round its coefficients to two decimal places.Determine all second order partial derivatives for f(x,y) =in3xy*3b) obtain a probility distribution of the sum of spot when a pair of dice is rolled
- What can you conclude about a real function f(x,y) that has continuous partial derivatives at a point (x,y)?There is a function f(x,y)=3√x3 + y. a)Calculate the partial derivative f,x (x, y) at points different from the point [0, 0] in which it is defined.2nd order linear homogenous DE with constant coefficients