Question

Find a geometric power series for the function, centered at 0, by the following methods Rx) - 2+x (a) by the technique shown in Examples 1 and 2 Rx) - (b) by long division (Give the first three terms.) Need Help? Read T alk te Tutor - 0/2 points Previous Answers LarCalcET6 9.9.004. Find a geometric power series for the function, centered at 0, by the following methods - 5- (a) by the technique shown in Examples 1 and 2 Mx) - (b) by long division (Give the first three terms.) Need Help? Submit Answer Practice Another Version

Answer 1

By flu)= 1 the centred at o. Maclaurin series method $100 = 1 2+1) ( +2) f(x) = ( 11 ) - interni t'o)= - 4 f") = (is) antrot"= 24 fwrite to P'w for 24 - 12o NI 7 (21)= 720 + Now get , use the calculated values to a polynomiol (geometric series)

w ******* * 31 41 0 16 finally simplifying we get the final fon ******* answer - - 16 32 (-1) 2'' no 7+1 1 + 2 4

. ful= f / centred at a By maclaurin series expansion f(u) = . fro) = 4/5 5-1 f' x)= ( 2 ) = 5; 101 - 12 (01- {"n) = le : fio) f" w lang ang fio) = f (x) = ( 2 ) = -26 4 100 = as a values to get Now, use the calculated a polynomial 96 3125 x 42

finally, after ximplifying we get the final answer f(x) - 4 + axt 4 n 25 125 t 4 625 + 4 nt .. " 3125 f(x) = Ann no 50 527 n. nzo bot (ii)