Question

Assignment 6: Problem Previous Problem Problem List Next Problem (1 point) Find the Maclaurin series for the function f(x) = 4x²e-4x in the form (f(x) = 00 Cmx"). Notice if a coefficient requested below is missing in the series then that coefficient is zero and you should enter 0. Find the individual coefficients Now give the general term as a formula involving n

Answer 1

We know that, .

- + - + 1+ +I= 3 -

Thus, and finally,

(-4r)" -= 1 – 4.0 +42 -43 +...+(-4)" +... η! n=0

4.02e-46 = 4.12 4.0 z" )" 4n+12+2 -= (-1)An-1 (n − 2)! n =0 412 - foam to podmiet... +(-1)"go--27 +..

Therefore,
Co=0
,
c =0
, $c_2=4$ ,
C3 = -16
,
C4 = = = 32
and $c_5=-\frac{4^4}{3!}=-\frac{128}{3}$ . Also,
n = (-1)"_ (n − 2)!
.