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Attempts This lost can only be taken once. Force Once started, this test must be completed in one sitting. Do not leave the test before clicking Save a Completion Your answers are saved automatically. Remaining Time: 1 hour, 29 minutes, 20 seconds. Question Completion Status: Moving to another question will save this response. Question 1 [The Macturin Sereis for the function F(x), M(x) = f(0) + f(O)x+90x+10 a. Find the first four nonzero terms of the Maclaurin series (a = 0) of the function f(x) = 0 b. Use power series operation to derive the Macluurin series of the function S(x)==" c. Use power series operation to derive the Macluurin series of the function f(x)=x'e' Τ Τ Τ • 3 (12pt) • T. from Part() (Write the implified from from Part() (Write the world Arial Path: P » A Moving to another question will save this response.

you can skip number 3

Answer 1

1.

a fin) en the function fin) is. Maclaunin series for f10) + f'o) 7 + +"(0) nett f() xt--- 3! f(x) = 2! - e = 1 +16= ex , +10) f'(a) = f'(o) = e = 1 f(n)co) = e = 1 fin) (x) = nonzero terms are first foun so, fin) It ut + rez = f(n) е 3 for fire) n. The maclaunin series fm (o) e n f(x) = swi n! neo 1 flo) tir) e 32 t'in) = 3 en f" (n) = 3' eju 3 #10) "(0) = 32 f(") (o)=3" FC") (n) = 3" 23 CS Scanned with CamScanner

co ex E 3 1 1 x n=0 Ĉ fin) = x3 en t'in = re? (x+3) en +10) = 0 t'10) t'14) = x(x² +64 +6) en tico) = (x3 + gx? +184 +6) epe 6 t" (O) f (4) = (x +12%? + 36% +24) e (n) +40) 24. fing (0) - n(n-1) (0-2) The Maclaurin series of fix) es. E fico) ren - fiu) no x² eu re nin) (1-2) n! no x² ex = x² tay + us+ set 27 24 + CS Scanned with CamScanner