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show full and complete procedure HANDWRITTEN only. for part A) find and sketch the domain of the function
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- Show that the function f (x, y)=(2 + x-y) / [1+ 2x ^ 2)+(3y ^ 2)] ∈R has a limit at (0,0).A function h(x, y) is defined by h(x,y)=(x^2 y)/(〖7x〗^6+y^3 ). Verify the limit over h(x, y) exists at the origin along y = x^2? In either case write also the reason.Show that the function f(x,y)=8x^2 y subject to 3x−y=9 does not have an absolute minimum or maximum. (Hint: Solve the constraint for y and substitute into f.) Solve the constraint for y. y = ? Substitute into f. f(x,y)= ? Determine the behavior of f as x approaches −∞. limx→−∞f(x,y)= ? Determine the behavior of f as x approaches ∞. limx→∞f(x,y)= ? Does this show that f does not have an absolute maximum or minimum? 1. No 2. Yes
- Let y(t) be the solution of dy/dt = 0.3y(2 − y) with y(0) = 1. Determine limt→∞ y(t) without solving for y explicitly.Suppose that the quadrature formula has degree of accuracy atleast 2 integral f(x)dx with upper limit 2 and lower limit -2 = a1f(−2) + a2f(0) + a3f(2) Use the definition of degree of accuracy to determine the constantsa1, a2, a3, and then determine the exact degree of accuracy of the quadratureformula. Is there any quadrature formula that has higher degree of accuracyand that also uses three functional evaluations?Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim (x, y, z)→(0, 0, 0) yz x2 + 4y2 + 4z2
- calculate the limits at x = a of the functionsConsider the following boundry value problem for an ODE:y'' = a, 0 < x < 1, where a is a constant.(a) Find the solution with boundary conditions y(0) = b1, y(1) = b2. Where b1 and b2 are arbitrary constants.(b) Is there any solution with boundary condition y'(0) = b1, y'(1) = b2? What is the necessary condition in order for the BVP to have a solution?Solve for A and B so that F(x) has a limit at both x=2 and x=4