Find the Taylor Series for 28^(3/5) Up to First Order – Tips & Suggestions

In summary, a Taylor Series is a way of representing a function as an infinite sum of polynomial terms to approximate its value at a specific point. To find the series, you need to calculate the function's derivatives and plug them into the general form. The first order refers to the first term in the series, which represents the value of the function at the given point. It is possible to find the Taylor Series for a function up to a certain order, but it can only provide an approximation, never an exact value.
  • #1
peripatein
880
0
Hello,

What polynomial should I use for finding Taylor series for 28^(3/5) up to the first order? I mean, aside x^3 around 2. Any suggestions?
 
Physics news on Phys.org
  • #2
Use the Taylor series of f(x)=x^(3/5) around a=32 (=2^5).

ehild
 
  • #3
Did you not mean to write =2^3 (Instead of "=2^5")?
 
  • #4
I know that 32=2^5.
 
  • #5
Yes, and that is the fifth power of an integer that is closest to 28. That's the point.
 

1. What is a Taylor Series?

A Taylor Series is a way of representing a function as an infinite sum of polynomial terms. This allows us to approximate the value of a function at a certain point by using a finite number of terms.

2. How do I find the Taylor Series for a given function?

To find the Taylor Series for a given function, you need to calculate the function's derivatives at a specific point and plug them into the general form of a Taylor Series. The general form is f(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3! + ...

3. What is the first order of a Taylor Series?

The first order of a Taylor Series refers to the first term in the series, which is f(a) in the general form. It represents the value of the function at the given point and serves as the starting point for the rest of the series.

4. How do I find the Taylor Series for 28^(3/5) up to first order?

To find the Taylor Series for 28^(3/5) up to first order, we need to calculate the first derivative of the function at a specific point. In this case, the first derivative is 3/5*28^(3/5-1) = 3/5*28^(-2/5). We then plug this into the general form of a Taylor Series to get the first order approximation.

5. Can I use a Taylor Series to find an exact value for a function?

No, a Taylor Series is an infinite series and can only provide an approximation of a function's value at a specific point. The more terms we include in the series, the closer the approximation will be to the actual value, but it will never be exact.

Similar threads

  • Calculus and Beyond Homework Help
Replies
4
Views
733
  • Calculus and Beyond Homework Help
Replies
27
Views
2K
  • Calculus and Beyond Homework Help
Replies
2
Views
1K
  • Calculus and Beyond Homework Help
Replies
6
Views
2K
  • Calculus and Beyond Homework Help
Replies
13
Views
2K
  • Calculus and Beyond Homework Help
Replies
9
Views
949
  • Calculus and Beyond Homework Help
Replies
12
Views
1K
  • Calculus and Beyond Homework Help
Replies
11
Views
2K
  • Calculus and Beyond Homework Help
Replies
10
Views
1K
  • Calculus and Beyond Homework Help
Replies
3
Views
879
Back
Top