By Hans Sagan

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15. 13 by choosing a = 28°. 13 and (c) compare with the exact value and the value obtained from the GregoryNewton formula. (a) The central difference table is shown in Fig. 2-16. k Yk Ayk -3 -2 -1 43,837 0 46,947 A2Yk A3yk -13 -14 -1 42,262 1,575 45,399 1,562 1,548 1,534 48,481 1 1,519 2 0 -14 -1 -15 50,000 Fig. 2-16 (b) Here k = 0 corresponds to 28°, k = 1 corresponds to 29°, k = -1 corresponds to 26°, etc. 4. 4 = 105 sin (28° 24') 1 1 f k(2) WD 110 + 2(Ay-I+AY0) 1! + Azy (1,548 + 1,534) (Z 46,947 + 1 2 ( 2!

Determine whether (a) M and (b) µ commutes with A, D and E. 100. Show that (d) 82f(x) (a) V2 = (AE-1)2 = A2E-2, (b) V n = AnE-n. o Sxn 2 1 + 4 - dny ? dxn Explain. (a) M = j(1 + E) _ E - JA, (b) µ = M/E112. (a) A = µ8+- 82, (b) A2m+1 = Em[1182m+1+48M+21. 101. (a) If A and B are any operators show that (A - B) (A + B) = A2 - B2 + AB - BA. (b) Under what conditions will it be true that (A - B)(A + B) = A2 - B27 (c) Illustrate the results of parts (a) and (b) by considering (A2 - D2)x2 and (A - D)(A + D)x2.

N! are all zero, then R. - 0 and yk is a polynomial of degree n in k. k 1! + 2! 9]. INTERPOLATION AND EXTRAPOLATION Often in practice we are given a table showing values of y or f (x) corresponding to various values of x as indicated in the table of Fig. 2-3. Z xo x1 ... 1 ... 1/y Fig. 2-3 < xp. e. xo < xl < An important practical problem involves obtaining values of y [usually approximate] corresponding to certain values of x which are not in the table. e. we suspect some underlying law of formation which may be mathematical or physical in nature.