Homework 11.9: pp 775--, #4, 22, 26

#4:

f[x_]:=5/(1-4x^2)
k=10
g[x_]:=5(∑_(n=0)^k)(((4x^2))^n)
Plot[{f[x],g[x]},{x,-.5, .5}]
Plot[{f[x]-g[x]},{x,-.5, .5}]

#22

f[x_]:=Log[x^2+4]
k=20
g[x_]:=Log[4]-(∑_(n=1)^k)(((((-1))^n)(((x/2))^(2n)))/n)
Plot[{f[x],g[x]},{x,-2, 2}]
Plot[{f[x]-g[x]},{x,-2, 2}]

#26:

f[x_]:=NIntegrate[t/(1+t^3),{t,0,x}] 
f[x]
N[f[0]]
N[f[.3]]
k=10
g[t_]:=(∑_(n=0)^k)(((((-1))^n)(((t))^(3n+2)))/(3n+2))
g[t]
N[g[0]]
N[g[.3]]
Plot[{f[x],g[x]},{x,-1, 1}]
Plot[{f[x]-g[x]},{x,-1, 1}]