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- Find thearea bounded by x=y^2 and y=-x^2Determine the value of x within the interval (0, 1) that minimizes the function f = (x –1)(x –2.5) to within ± 0.025 by .(a) the Fibonacci method and (b) the golden section method.Show that F (x, y) = x2 + 3y is not uniformly continuous on the whole plane.Hint: You must prove that there are pairs of points, arbitrarily close together, on which thevariation of F is large, for example, (n, 0) and (n + 1/n, 0).
- considering the nonhomogenous 2ndorder ode y'' + 4y = 10sin(9pi x t)Find k so that f has a critical number at x=3A 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)
- If after evaluating the Wronskian of the functions y1 and y2 the result is W=7x2+19 in the interval I = ]-∞,0[ Determine if the functions y1 and y2 are Linearly independent or Linearly dependent1 Show that the square integrable function f(x) = sin( πk log x/ log 2 )for k ≥ 1 are orthogonal over the interval 1 ≤ x ≤ 2 with respect to the weight function r(x) = 1/ x . Obtain the norms of the functions and construct the othornormal set.Compute the Wronskian for 2t^2y''+3ty'-y=0
