Answer by Lee Mosher for When does the remainder term in the taylor series go...
There is no easy answer to the question of how to prove that the remainder term goes to zero. It is an art. The art of bounds, the mathematical art known as "Analysis". If you try some examples you may...
View ArticleAnswer by JoeyBF for When does the remainder term in the taylor series go to...
The idea behind Taylor series is to approximate an $N+1$-times continuously differentiable function at a point by using the information given by the derivatives at that point. For example, when a...
View ArticleAnswer by Tom R for When does the remainder term in the taylor series go to...
Hint: The Taylor series is sometimes called a Taylor polynomial. What is the Taylor series of a polynomial function?
View ArticleWhen does the remainder term in the taylor series go to zero?
When does the remainder term in the taylor series go to zero?Theorem: Let $f\in C^{N+1}([\alpha,\beta])$ and $x,x_0\in(\alpha,\beta)$....
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