Aproximando funciones con polinomios de Taylor y límites de error
Examples
Lessons
Free to Join!
StudyPug is a learning help platform covering maths and science from primary all the way to second year university. Our video tutorials, unlimited practice problems, and step-by-step explanations provide you or your child with all the help you need to master concepts. On top of that, it's fun — with achievements, customizable avatars, and awards to keep you motivated.
Easily See Your Progress
We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.Make Use of Our Learning Aids
Earn Achievements as You Learn
Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.Create and Customize Your Avatar
Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.
Topic Notes
Para aproximar una función con un polinomio de Taylor de grado n centrado en a=0, usa:
f(x)≈f(a)+f′(a)(x−a)+2!f"(a)(x−a)2+⋯+ n!fn(a)(x−a)2
Donde:
Pn(x)=f(a)+f′(a)(x−a)+ 2!f"(a)(x−a)2+⋯+n!fn(a)(x−a)2 es el polinomio de Taylor.
Para encontrar la diferencia entre el valor real y el valor aproximado busca por el término del error, el cual es definido como:
Rn(x)= (n+1)!fn+1(z)(x−a)n+1
A esta se le llama la fórmula de Lagrange.
Nota que sumando el polinomio de Taylor con el error te da el valor exacto de la función. En otra palabras:
f(x)=Pn(x)+Rn(x)
f(x)≈f(a)+f′(a)(x−a)+2!f"(a)(x−a)2+⋯+ n!fn(a)(x−a)2
Donde:
Pn(x)=f(a)+f′(a)(x−a)+ 2!f"(a)(x−a)2+⋯+n!fn(a)(x−a)2 es el polinomio de Taylor.
Para encontrar la diferencia entre el valor real y el valor aproximado busca por el término del error, el cual es definido como:
A esta se le llama la fórmula de Lagrange.
Nota que sumando el polinomio de Taylor con el error te da el valor exacto de la función. En otra palabras:
2
videos
remaining today
remaining today
5
practice questions
remaining today
remaining today