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- Let S={(x,y)∈N×N|(2−x)(2−y)<2(4−x−y)}.Prove that S=TS=T, where T={(1,1),(1,2),(2,1),(1,3),(3,1)}Find S ∩ T, (S ∩ T)c, Sc ∩ Tc, S ∪ T, (S ∪ T)c, and Sc ∪ Tc (1) S = (0, 1), T = [1/2, 3/2] (2) S ={x |x2 > 4}, T = {x |x2 < 9} (3) S =(-∞, ∞), T = Ø (4) S =(-∞, -1), T = (1, ∞)if zi = ayi for i=1,2,...,n, show that z=ay as in 3.3.
- Let, w = (xy)/z and x = 2s + t, y = st, z = 2s - t Find (photo attached):Compute ∇ƒ(-1, 2, 1), where ƒ(x, y, z) = xy/z.Suppose that receiving stations X, Y, and Z are located on a coordinate plane at the points (4,4), (−12,−4), and (−6,9), respectively. The epicenter of an earthquake is determined to be 5 units from X, 13 units from Y, and 10 units from Z. Where on the coordinate plane is the epicenter located?
- Find the clamped cubic spline that interpolates (0,0),(1,1),(2,2) and satisfies the condition: s’(0) = 1 and s’(2) = 1.Number 7 Identify if homo, varsep, exact, linear in z, linear in t, Bernoulli in z and bernoulli in t, and find the DELet D4 = <r, f | r 4 = e = f 2, rf = fr-1>. Verify that6 * [3 * (r, 0), ( f, 0), 3 * (r, 0), (e, 1)]is a Hamiltonian circuit inCay({(r, 0), (f, 0), (e, 1)}:D4 ⨁ Z6).