3.01.4.Literacy - Approximation Authors Bill Davis Horacio...

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Approximation Authors: Bill Davis, Horacio Porta and Jerry Uhl ©1996-2007 Publisher: Math Everywhere, Inc. Version 6.0 3.01 Splines LITERACY · L.1) What is the order of contact between e x and 1 + x at x = 0 ? What is the order of contact between e x and 1 + x + x 2 2 at x = 0 ? What is the order of contact between e x and 1 + x + x 2 2 + x 3 3 ! at x = 0 ? For your information: 3 != 3 * 2 * 1 = 6 . · L.2) What is the order of contact between Sin @ x D and x - x 3 3 ! at x = 0? · L.3) What is the order of contact between Cos @ x D and 1 - x 2 2 at x = 0? What is the order of contact between Cos @ x D and 1 - x 2 2 + x 4 4 ! at x = 0? For your information: 4 != 4 * 3 * 2 * 1 = 24. · L.4) What is the order of contact between Log @ x D and H x - 1 L - H x - 1 L 2 2 at x = 1? (For your information: D AI 1 2 H x - 1 L 2 M , x E = H x - 1 L .) What is the order of contact between Log @ x D and H x - 1 L - H x - 1 L 2 2 + H x - 1 L 3 3 at x = 1? (For your information: D AI 1 3 H x - 1 L 3 M , x E = H x - 1 L 2 .) · L.5) You have two curves y = f @ x D and y = g @ x D with f @ a D = g @ a D , and you want to make a transition from the f @ x D curve to the g @ x
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