A question about Taylor series expansions

In summary, Taylor series expansions are mathematical representations of functions that use an infinite sum of terms. They are used to approximate complex functions and calculate unknown values at any point based on known values at a specific point. To calculate a Taylor series expansion, the derivatives of a function at a specific point are evaluated and plugged into the general formula. These expansions have many applications in various fields such as math, physics, and engineering, but they also have limitations. They only work for smooth functions and provide local approximations.
  • #1
hefnrh
2
0
Find the Taylor series expansions for f(x)=x*e^(-x^2) about x = -1
-(1/E) - (x + 1)/E + (x + 1)^2/E + (5 (x + 1)^3)/(3 E) + (x + 1)^4/(
6 E) - (23 (x + 1)^5)/(30 E) - (29 (x + 1)^6)/(90 E) + (
103 (x + 1)^7)/(630 E)...
This is the answer from Mathematica but i don't know how it goes.
Can anybody help me?
Thanks.
 
Last edited:
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  • #2
Try posting your question again, but when you do so use the required format for homework.

Don't forget to show the relevant equations and show that you have done some work on the problem.
 

1. What are Taylor series expansions?

Taylor series expansions are mathematical representations of functions using a sum of infinite terms. They are used to approximate functions and calculate values of a function at any point based on its derivatives at a specific point.

2. What is the purpose of using Taylor series expansions?

The main purpose of using Taylor series expansions is to approximate complex functions with simpler ones in order to make calculations easier. They are also used to find unknown values of a function at any point based on its known values at a specific point.

3. How is a Taylor series expansion calculated?

A Taylor series expansion is calculated by taking the derivatives of a function at a specific point, evaluating them at that point, and then plugging those values into the general formula for a Taylor series. The formula is: f(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3! + ...

4. What are the applications of Taylor series expansions?

Taylor series expansions have many applications in mathematics, physics, and engineering. They are used to solve differential equations, approximate functions in calculus, and analyze the behavior of physical systems. They are also used in computer graphics and signal processing.

5. Are there any limitations to using Taylor series expansions?

Yes, there are limitations to using Taylor series expansions. They only work for smooth functions, meaning functions that have continuous derivatives of all orders. They also only provide local approximations, meaning they are only accurate near the point at which they are calculated.

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