Maclaurin series

[Atrox]

Hi,

I am really not good at math,

So I am trying to understand how to solve the image:

formula for Maclaurin series is:
$$f(x) = \sum_{n=0}^\infty \frac{f^{(n)}(0)}{n!}x^n$$
do I have to do the following:
f'(x)+f''(x)+f'''(x)+...

I can basically take the derivative of the following at any point, for example 0, and then continue the above expression? is that correct?


thanks.

 

[BeansNRice]

Trying to imagine how someone who's "really not good at math" has been tasked with a problem involving the Maclaurin series but whatever.

Yes, what you've outlined is correct. Take a few derivatives of the arctan, evaluate them at zero, see if you can detect a pattern (there is one).

Then write out f(x) as the series based on the formula you wrote.

Now substitute (-x) in for (x) in that series and evaluate what happens.

 

[Steven G]

Before you can answer such a problem you need to know the definitions for even and odd functions. You can't play the game unless you know the rules!

Think real hard about this definition and how you expect the graph to look like:
A function f(x) is said to be even if f(-x) = f(x). Remember that the height of a function is the y value also know as the f(x) value. In our function it turns out that f(-1) = f(1), f(-sqrt3)= f( sqrt3), f(-pi) = f(pi), ... This means that when you plug in say 5 or -5 into f(x), then you get back the say y value (which is the height). Can YOU draw any graph which is even??

A function g(x) is said to be odd if g(-x) = - g(x). So, for example g(-3) = -g(3). What can you tell me about the y values for x= 3 and x=-3?

Please respond back with the answers do my questions and include a graph of an even function and an odd function.