**Infinity X5**

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We thus have a decomposition (stratification): X5 = X5 ⋃ i,j Dij ⋃ i,j,k,l Qij,kl, where the union over the i, j runs over the 10 pairs 1 To summarize, the divisor at infinity X5 −X5 consists of 10 copies Dij of X4 and 15 copies Qij,kl of X3, which is F. R O M Z E R O TO INFINITY . 1 – x 1 – x2 1 – A – x2 + x' 1 – X" 1 – A – x + x' – x + x* + x” – x" 1 – X = x* + x4 + x5 – x6 1 – x4 1 – X = x* + x* + x” – x" – x* + x2 + x" — X" x” + x10 1 – A – x* + 2x” – 3:3 x” + x10 1 – X" 1 – A – x* +2x” – 3:3 x” + Let us try for example to write down 60 as a product: 60 = 6 X l0 Both 6 and 10 can be further split into factors, 6:2 ><3and10=2.X5 and writing these in place of 6 and I0 we have 60 = 2 X 3 X 2 X 5 where all its factors are prime numbers.x5/5! (14) In the next step, the correction term is introduced to correct the deficiency of the approximation for the sinechord. So that the next approximation is rq – rsinq ≈ x3/3! – x5/5! – x7/7! (14a) Continuing in this way, ad infinitum, we have 40.00 x3 3,000.00 0.00 −0.50 infinity 2.96 x4 0.00 0.49 −0.50 0.49 infinity x5 0.00 6.56 −11.90 6.56 infinity x6 1,000.00 0.00 −10.40 infinity 0.49 x7 0.00 0.91 −0.20 0.91 infinity x8 1,000.00 0.00 −1.60 infinity 0.80 x9 25.00 0.00 −400.00 infinity The limit off as x approaches infinity is negative infinity or limx!1f.x/ D 1 means that for.every M2 R there is an N 2 R f.x/ D 1 means that for every M 2 R there is an N 2 R such that if x is in the domain off with x < N, then f.x/ < M. xC3 .x5/2 D 1?Graph of the polynomial y = x5 − x + 1. the actual example y = x5 − x + 1. Since the curve passes from below to above the xaxis, and the xaxis has no gaps, the curve necessarily meets the xaxis. That is, there is a real value of x for which x5 A I0I4L >TqUI4TKNft (1(411 AI XI + X2 + X3 + X4 + X5 + X6 + X7 OBJECT TO ) + .7061 XI + .0000 X2 .0025 X3 .0516 CURRENT ALLOWABLE ALLOWABLE COEF INCREASE DECREASE 7.1 1.00 INFINITY 1.547073 X2 1.00 INFINITY y2 + x2y = x5 + x4 + x Ci3:y2 : y2 + x2y = x5 + x4 + x + 1 . V2 + x2y + xy + y = x5 + x Ci8: y2 + x2y + xy +.y = x5 + x + 1 . Each of these curves is nonsingular affinely and the point at infinity in each model is singular. The nonsingular model is the MAX 13 XI ♢ 16 X2 ♢ 16 X3 ♢ U X* + 39 X5 SUBJECT TO 11 X1 ♢ 53 X2 ♢ 5 X3 t 5 X4 ♢ 29 X5 < = 40 2) 3 X1 ♢ 6 X2 » 5 X3 14.000000 INFINITY 12.063268 X5 39.000000 51 .666668 30.245283 RIGHTHAND SIDE RANGES ROW CURRENT