The discussion revolves around the graphing of the hyperbolic cosine function, cosh(x), using its Taylor series expansion. Participants explore how the approximation improves with additional terms and consider the implications of using the series for both positive and negative values of x.
The discussion is active, with participants sharing insights about the symmetry of the function and the limitations of finite Taylor series in capturing the behavior of cosh(x) for large values of x. Some guidance is offered regarding experimentation with different numbers of terms in the series.
There is an emphasis on the nature of the Maclaurin series and its even-degree terms, which leads to the symmetry of the graph about the y-axis. Participants are also considering the theoretical aspects of approximation limits.
The more terms you use in the Taylor series (really, what you have is the Maclaurin series), the closer your Taylor/Maclaurin polynomial will approximate the graph of y = cosh(x).Vitani11 said:Homework Statement
For example
cosh(x) = 1+x2/2!+x4/4!+x6/6!+...
Homework Equations
The Attempt at a Solution
So plugging in x=0 you get that coshx = 1 at the origin. The approximate graph for the coshx function up to the second order looks like a 1+x2/2! graph, but what about graphing coshx to the term afterwards? and so on.
See the graphs on this page: https://en.m.wikipedia.org/wiki/Hyperbolic_functionVitani11 said:Also, what about its negative values? What about the point where cosh slope changes direction? Etc.
Vitani11 said:Homework Statement
For example
cosh(x) = 1+x2/2!+x4/4!+x6/6!+...
Homework Equations
The Attempt at a Solution
So plugging in x=0 you get that coshx = 1 at the origin. The approximate graph for the coshx function up to the second order looks like a 1+x2/2! graph, but what about graphing coshx to the term afterwards? and so on.