1. ESCUELA DE INGENIERÍA DE PETROLEOS

2. ESCUELA DE INGENIERÍA DE PETROLEOS A Taylor series is a series expansion of a function about a point. A one-dimensional Taylor series is an expansion of a real function about a point is given by

3. ESCUELA DE INGENIERÍA DE PETROLEOS It is common practice to use a finite number of terms of the series to approximate a function. The Taylor series may be regarded as the limit of the Taylor polynomials. Taylor's theorem (actually discovered first by Gregory) states that any function satisfying certain conditions can be expressed as a Taylor series.

4. ESCUELA DE INGENIERÍA DE PETROLEOS The Taylor (or more general) series of a function about a point up to order may be found using Series[ f , x , a , n ]. The th term of a Taylor series of a function can be computed in Mathematica using SeriesCoefficient[ f , x , a , n ] and is given by the inverse Z-transform

5. ESCUELA DE INGENIERÍA DE PETROLEOS Taylor series of some common functions include = = = = = =

6. ESCUELA DE INGENIERÍA DE PETROLEOS To derive the Taylor series of a function , note that the integral of the st derivate of from the point to an arbitrary point is given by

7. ESCUELA DE INGENIERÍA DE PETROLEOS If the expansion is known as a Maclaurin series . Maclaurin series are a type of series expansion in which all terms are nonnegative integer powers of the variable. Other more general types of series include the Laurent series and the Puiseux series.

9. ESCUELA DE INGENIERÍA DE PETROLEOS Reemplazando por xi=2 Rta

11. ESCUELA DE INGENIERÍA DE PETROLEOS Rta

12. ESCUELA DE INGENIERÍA DE PETROLEOS b) Completar la siguiente tabla para P 3 (x) y para f(x) (Utilizar radianes). x -0,75 -0,5 -0,25 0 0,25 0,5 0,75 f(x) 2,4189 2,0943 1,8235 1,5708 1,3182 1,0472 0,7227 P 3 (x) 2,3911 2,0916 1,8234 1,5708 1,3182 1,0499 0,7505 %E 1,1471 0,1319 3,9713x10 -3 2,3384x10 -4 6,0512x10 -3 0,2644 3,8400

13. ESCUELA DE INGENIERÍA DE PETROLEOS c) Dibujar sus gráficas en los mismos ejes coordenados.