24. Let f be a function such that f'(x) Maclaurin series for f? = sin 9 (A) x - + 10 216 9 X (B) 2x 5 x + 12 (C) (D) 3333 x7 + 21 55 11 42 + 1320 n(x²) and f(0) = 0. What are the first three nonzero terms of the

Find the MacLaurin Series for f (x) = cos(2/x) (-1)"(2x)" (2n)! -x+ 등-. 3 = 1 – x + 6 90 .. (-1)"(4x)" (2n)! = 1-2x + 을x2-.. 2 2 4 Zn=0 45 .. (-1)"x2" (2n)! .2 = 1 – * + - X. Zn=0 2 24 720 .. (-1)"x" (2n)! = 2 – x + - 100 3 Zn=0 720 ..

Consider the general Maclaurin's series formula xn f(x)=f(0) + xf'(0) + 27ƒ”(0) + ... + 27 ƒ(n)(0) + ... (where f(x) indicates the nth derivative off). Use the formula to find the first five terms of the Maclaurin's series for e^(2x) find the value of e^(2x) when x=1 and also compare the exact value of e^(2x) when x=1 Explain how the accuracy of the Maclaurin's series approximation could be improved.

1. Find the first 3 terms in the Maclaurin series for the function f(x) = sin2x 2. Find the first 3 terms in the Maclaurin series for the function f(x) = xe^-x 3. Find the first 3 terms in the Maclaurin series for the function f(x) = x/(1+x²)

Find the first three terms of the Maclaurin series of f (x) and use it to calculate f ^(3)(0).

Q2// Find the Maclaurin series of the function www f(x) = x² sinx ?

The function f(x)=3xarctan(6x) is represented as a power series (image) Find the first few coefficients in the power series.