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- Expand x^2y+3y-4 about the point (-1,2) by Taylor's theoremFind the perticular number or orthogonal trajectories of x2+cy2=1 passing through the point (2,1). 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).
- A manufacturing company employs two devices to inspect output for quality controlpurposes. The first device can accurately detect 99.2% of the defective items it receives, whereasthe second is able to do so in 99.5% of the cases. Assume that five defective items are producedand sent out for inspection. Let X and Y denote the number of items that will be identified asdefective by inspecting devices 1 and 2, respectively. Assume that the devices are independent.Find: a. f Y|2(y) b. E(Y│X=2)= and V(Y│X=2)=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 dependentconstruct a suitable Liapunov function of the form ax2 + cy2, where a and c are to be determined. Then show that the critical point at the origin is of the indicated type. 2.dxdt=−x3+2y3,dydt=−2xy2; stable (at least)dxdt=−x3+2y3,dydt=−2xy2; stable at least
- Is ((z^2+2z+2)^(1/2))/(z^2-4z+3) an analytic function in |z|>2 and |z|<2 using cauchy riemann equation?General Directi0n: F0r activities that inv0lve s0luti0n to problems, perform the steps in conducting hypothesis testing such as stating of problems and hypothesis, and so on.Use algebraic methods to determine the critical value(s) of f(x)= x/(x^2-x-2). Give your answers in exact form.