Tuesday, 7 May 2019

calculus - Intuition behind Taylor/Maclaurin Series

** This is a different question than Intuition explanation of taylor expansion? **



I understand some of the intuition behind a Taylor/Maclaurin expansion. More specifically, I understand that adding higher and higher degree polynomials will add more 'turning points' on a graph to better represent the curves of the function you wish to approximate.



I don't understand why




a.) you add the terms; shouldn't adding terms shift the graph left/right, up/down? In addition to the question of shifting the graph, I just don't understand why you would add more terms, rather than just change your first term accordingly.



I now understand the above, thanks to microarm15 and Nicholas Stull. I now just do not understand part b of this question



b.) the terms added are the successive derivatives of the function. What does adding successive derivatives mean/give you?



Any help on the matter is greatly appreciated.
Thanks!

No comments:

Post a Comment

real analysis - How to find $lim_{hrightarrow 0}frac{sin(ha)}{h}$

How to find $\lim_{h\rightarrow 0}\frac{\sin(ha)}{h}$ without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...