Make a Power Series
\frac{3}{1+x}
\sum_{n=0}^\infty (-1)^n 3x^n
\text{With IOC } -1<x<1
Find the 4th degree Maclaurin series of
f(x) = 3\cos(x)
M_4 = 3-\frac{3}{2}x^2+\frac{1}{8}x^4
Find the 3rd degree Taylor series centered at 3 of the function
f(x) = 2x^3-4x^2+5x-4
T_3 = 29+35(x-3)+14(x-3)^2+2(x-3)^3
\frac{x^3}{1-x^2}
\sum_{n=0}^\infty x^{2n+3}
\text{With IOC } -1<x<1
Find the 4th degree Maclaurin series of
f(x) = (2x+2)^4
16+64x+96x^2+64x^3+16x^4
Find the 4th degree Taylor series centered at 2 of
f(x) = 3e^{x-2}
T_4 = 3+3(x-2)+\frac{3}{2}(x-2)^2+\frac{1}[2}(x-2)^3+\frac{1}{8}(x-2)^4
\frac{x}{4-x}
\sum_{n=0}^\infty \frac{(-1)^n}{4^{n+1}}x^{n+1}
\text{With IOC } -4<x<4
Find the 2nd degree Maclaurin series of
f(x) = \frac{1}{x^2+x+1}
M_4=1-x
Find the 2nd degree Taylor series centered at
\frac{\pi}{2} \text{ of } f(x) = \sin(\cos(x))
T_2 = -(x-\frac{pi}{2})
\frac{4x^3}{3+x^4}
\sum_{n=0}^\infty (-1)^n \frac{4}{3^{n+1}} x^{4n+3}
\text{WITH IOC } -3^{1/4}<x<3^{1/4}
Computer the second degree Maclaurin series for
f(x) = xe^{2x}
M_4 = x+2x^2
Find the 4th degree Taylor series centered at 1 of
f(x) = \ln(4-3x)
T_4=-3(x-1)-\frac{9}{2}(x-1)^2-9(x-1)^3-\frac{81}{4}(x-1)^4