%typeset_mode True
# make a taylor polynomial of the function ln(1+x) with x centered at 2, degree 9 taylor(ln(1+x), x, 2, 9)
1771471(x−2)9−524881(x−2)8+153091(x−2)7−43741(x−2)6+12151(x−2)5−3241(x−2)4+811(x−2)3−181(x−2)2+31x+log(3)−32
# taylor polynomial of e^x about 1, degree 4 taylor(e^x,x,1,4)
241(x−1)4e+61(x−1)3e+21(x−1)2e+(x−1)e+e
# taylor polynomial of cos(x) centered at pi/2, degree 4 (note that it's doing a little simplifying, unfortunately) taylor(cos(x),x,pi/2,4)
21π−481(π−2x)3−x
# taylor polynial of ln(x^2) cntered at 1, degree 4 taylor(ln(x^2),x,1,4)
−21(x−1)4+32(x−1)3−(x−1)2+2x−2
N(integral(sin(x)/x,x,0,1))
0.946083070367