Answer by davidlowryduda for Cannot understand calculations (Taylor's Theorem)
This is a case where an easy calculation really means a tedious but straightforward calculation that I don't want to write down, and not an obvious and simple calculation. There is loads of...
View ArticleAnswer by José Carlos Santos for Cannot understand calculations (Taylor's...
You have that $F(t)$ is a constant ($f(x)$) plus$$-f(t)-(x-t)f'(t)-\frac{(x-t)^2}2f''(t)-\cdots-\frac{(x-t)^n}{n!}f^{(n)}(t).$$Forget the constant; if you differentiate it, you get $0$. Then:if you...
View ArticleAnswer by Kaind for Cannot understand calculations (Taylor's Theorem)
$\big( f^{i}(x) \frac{(x - t)^i}{i!} \big)' = f^{i+1}(x) \frac{(x - t)^i}{i!} + f^{i}(x) \frac{(x - t)^{i-1}}{(i-1)!}$ by product rule.Sum over $i$, to see that the series is telescoping.
View ArticleCannot understand calculations (Taylor's Theorem)
I have been studying Taylor's Theorem by Bartle's book. However, i cannot understand some simple(?) calculations, and that is really bothering me.Theorem (as stated in the book):Let $n \in \mathbb{N},$...
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