### Related

t: taylor ((1 - x^10)...

Calculate

Calculate

t: taylor (1 + x + x^...

t: taylor(-(83787*x^...

Calculate

f(x):=tan(x);

h:taylor(f(x),x,0,10);

Calculate

f(x) := %e^(-x*x);

t(x) := taylor(f(x), ...

t(x);

Calculate

Calculate

Calculate

f(x) := e^(-x*x);

n : 64;

g(x) := taylor(f(x), ...

Calculate

t: taylor ((1 - x^9)/...

Calculate

t: taylor(-1-3*x-7*x^...

Calculate

Run Example
```(%i1)pade(taylor(sin(x),x,0,7),7,1);
7       5        3
x  - 42 x  + 840 x  - 5040 x
(%o1)                  [- ----------------------------]
5040
(%i2) ```
Run Example
```fullratsimp (pade (taylor (exp (x), x, 0, 8), 4, 4));
4       3        2
x  + 20 x  + 180 x  + 840 x + 1680
(%o1)                [----------------------------------]
4       3        2
x  - 20 x  + 180 x  - 840 x + 1680
(%i2) ```
Run Example
```f(x) := x^(1/12);
1/12
(%o1)                            f(x) := x
(%i2) k : 6;
(%o2)                                  6
(%i3) n : 2 * k;
(%o3)                                 12
(%i4) t(x) := taylor(f(x), x, 1/3, n);
1
(%o4)                    t(x) := taylor(f(x), x, -, n)
3
(%i5) t(x);
1/12 11      1          1/12 11       1 2
1/12 11   (3    )   (x - -)   (11 (3    )  ) (x - -)
(3    )                    3                        3
(%o5)/T/ --------- + ----------------- - -----------------------
3              12                     96
1/12 11       1 3           1/12 11       1 4
(253 (3    )  ) (x - -)    (8855 (3    )  ) (x - -)
3                           3
+ ------------------------ - -------------------------
1152                       18432
1/12 11       1 5              1/12 11       1 6
(83237 (3    )  ) (x - -)    (4910983 (3    )  ) (x - -)
3                              3
+ -------------------------- - ----------------------------
73728                        1769472
1/12 11       1 7                 1/12 11       1 8
(49811399 (3    )  ) (x - -)    (4134346117 (3    )  ) (x - -)
3                                 3
+ ----------------------------- - -------------------------------
7077888                         226492416
1/12 11       1 9                    1/12 11       1 10
(392762881115 (3    )  ) (x - -)    (8405125655861 (3    )  ) (x - -)
3                                    3
+ --------------------------------- - -----------------------------------
8153726976                           65229815808
1/12 11       1 11
(90928177549769 (3    )  ) (x - -)
3
+ ------------------------------------
260919263232
1/12 11       1 12
(11911591259019739 (3    )  ) (x - -)
3
- --------------------------------------- + . . .
12524124635136
6                 5                  4                 3
(%o6) [(54650399895 x  + 596950521930 x  + 1174002693129 x  + 662800319244 x
2
+ 118357199865 x  + 5950198026 x + 49811399)
1/12               6                5                4                3
/(3     (36312509871 x  - 72625019742 x  + 60520849785 x  - 26898155460 x
2
+ 6724538865 x  - 896605182 x + 49811399)
13/12                5                 4                 3
+ 3      (184863686616 x  + 334897983000 x  - 651934740240 x
2
+ 360201386160 x  - 83848532040 x + 7177566648)
25/12                3                 2
+ 3      (293944743936 x  - 293944743936 x  + 97981581312 x - 10886842368)
37/12               2
+ 3      (62541434880 x  - 23037861888 x + 2832371712))]
(%i7) p(x) := pade(t(x), n/2, n/2)[1];
n  n
(%o7)                      p(x) := pade(t(x), -, -)
2  2
1
(%i8) pp(x) := bfloat(p(x));
(%o8)                        pp(x) := bfloat(p(x))
(%i9) pp(x);
6                    5                      4
(%o9) (1.0b0 (5.4650399895b10 x  + 5.9695052193b11 x  + 1.174002693129b12 x
3                     2
+ 6.62800319244b11 x  + 1.18357199865b11 x  + 5.950198026b9 x + 4.9811399b7))
6                    5
/(1.095872691135244b0 (3.6312509871b10 x  - 7.2625019742b10 x
4                   3                  2
+ 6.0520849785b10 x  - 2.689815546b10 x  + 6.724538865b9 x  - 8.96605182b8 x
5                  4
+ 4.9811399b7) + 3.287618073405733b0 (1.84863686616b11 x  + 3.34897983b11 x
3                    2
- 6.5193474024b11 x  + 3.6020138616b11 x  - 8.384853204b10 x + 7.177566648b9)
3                     2
+ 9.862854220217199b0 (2.93944743936b11 x  - 2.93944743936b11 x
+ 9.7981581312b10 x - 1.0886842368b10)
2
+ 2.95885626606516b1 (6.254143488b10 x  - 2.3037861888b10 x + 2.832371712b9))
(%i10) l : 2^-12;
1
(%o10)                               ----
4096
(%i11) r : 2^0;
(%o11)                                 1
(%i12) plot2d([(f(x)-pp(x))/f(x)], [x, l, r]);
plot```