I just dont know where to start!

  • Thread starter rcmbimp
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In summary: For the Maclaurin series, the criterion for convergence is that the series converges to the function.
  • #1
rcmbimp
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Non analytic function?

Homework Statement



I was set this question as part of an extra problem sheet by my maths teacher, and i don't know where to start. He said its like first year university maths standard, and gave me hints to use the maclaurins and binomial series. I am just a bit stuck... PLEASE HELP... I found an example of a non analytical function on this forum, but just confused me!

the question...

Consider the function
f(x) = "e− 1
x2 if x "= 0
0 if x = 0
.
Calculate the Maclaurin series of f and show that it does not converge to f(x) for x "= 0. In
particular f is not an analytic function.

Homework Equations



Maclaurins series
Binomial expansion

The Attempt at a Solution



I don't know where to start
 
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  • #3
woops... can't copy and paste!

Yes sorry it is an e^x...

Thanks for yuor reply, but I am still really stuck. I emailed my teacher the other day and he said to try find an example, and just understand it (or try to understand it).

Does anyone know where i could find a worked solution of this... preferablely with quotations as it goes along...

thanks
rcmbimp
 
  • #4
rcmbimp said:
Yes sorry it is an e^x...

Thanks for yuor reply, but I am still really stuck. I emailed my teacher the other day and he said to try find an example, and just understand it (or try to understand it).

Does anyone know where i could find a worked solution of this... preferablely with quotations as it goes along...

This page has some good examples regarding convergence of a series.
http://www.math.ubc.ca/~indurskis/math100/taylor/example6.html

Think about the purpose of expanding using a series and then think about the criterion for convergence.
 
Last edited by a moderator:

1. What is a non-analytic function?

A non-analytic function is a mathematical function that is not differentiable at one or more points. This means that the function's graph has a sharp corner, cusp, or other type of discontinuity at those points.

2. How do non-analytic functions differ from analytic functions?

Unlike non-analytic functions, analytic functions are infinitely differentiable at every point within their domain. This means that their graphs are smooth and have no sharp corners or discontinuities. Analytic functions also have a convergent Taylor series expansion.

3. What are some examples of non-analytic functions?

Some common examples of non-analytic functions include absolute value, step function, and the inverse tangent function. These functions have points of non-differentiability at certain points within their domains, making them non-analytic.

4. Why are non-analytic functions important in mathematics?

Non-analytic functions are important in mathematics because they provide a way to describe and model real-world phenomena that are not smooth or continuous. They are also used in physics and engineering to solve problems that involve sharp changes or discontinuities.

5. How can non-analytic functions be evaluated?

Since non-analytic functions are not differentiable at certain points, they cannot be evaluated using traditional calculus methods. Instead, they can be evaluated using numerical methods such as approximations, interpolations, or root-finding algorithms.

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