Find a Maclaurin series for f(x). (Use f* √ ₁ + 1³ d 1 f(x) = f(x) = x + +*12+Ë n = 2 (2n)! 2"n! (2n-1) for 135... (2n-3).) (−1)²−¹(2n)!x5n+1 ( 5n + 1) (2n − 1) (2n!) ²

Suppose that f(x) and g(x) are given by the power series f(x) = 2+ 2x + 4x² + 3x³ + ... and g(x) = 2+ 3x + 5x? + 3x³ + • ... By multiplying power series, find the first few terms of the series for the product h(x) = f(x) · g(æ)= co+ C1x + c2a² + c3æ³ + • ... Co = 4 Ci = C2 C3 II

im Y cosx tZx5 又ナ。 7x¢

Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. x3 f(x) = V11 + x AI (-1y9 2-4 - 6- n!11" + 1/2. 2n .. · (2n) ,n + 3 2(-1)". + n = 1 E (-1)n 1-3: 5 . · (2n – 1) n + 3 n!11" + 1/2. 2n .... 11 n = 1 1. 3. 5. .* · (2n – 1) n + 3 2 (-1)n + + 11 n!11" + 1/2. 2n n = 1 1· 3· 5. (2n – 1) n n!11" + 1/2. 2n ... + 11 n = 1 00 Σ > (-1)n + 1l:3.5.…. (2n – 1) , n!11" + 1/2 . 2n ... + 11 n = 1

Find the first four nonzero terms in the Maclaurin series for the function. f(x)=x sin(4x) 32 OA. 4x²+. OB. 4x-8x3 OC. 4x- 32 + OD. 4x2. 32 +4 + 2-32x + 128 15 512 15 + 128 15 1024 + -x8 315 4096 45 -x6 -x7 4096 315 +8 1024 -x8 315 ... Time Remaining.

Find the Maclaurin series for f(x) 18 8 8 8 n=0 n=0 n=0 n=0 æn+1 2n (−1)"mn 2n (−1)": "mn+1 2n xn 2n O None of these. = X 1+2/2

(2n)! 2"n!(2n-1) Find a Maclaurin series for f(x). (Use for 1:3· 5... (2n - 3).) f(x) = [ VI+e dt DO f(X) = x + X 12 + n = 2