Solve Maclaurin Series for f(x)= 1/(1+x+X2)

In summary, the Maclaurin series for f(x) = 1/(1+x+x^2) can be found by dividing 1 by the Maclaurin series of 1+x+x^2, or by finding the derivatives of f(x) and using the formula, which results in 1-x+x^3. The second method is accurate, while the first method would also be accurate if polynomial division is used correctly.
  • #1
Crazy Gnome
13
0

Homework Statement


Find the Maclaurin series for f(x)= 1/ (1+x+X2)


Homework Equations





The Attempt at a Solution



I think the book says I can just divide 1 by the Maclaurin series of (1+x+X2). And when i do this the original function is the answer (which makes sense).

But when I do it my finding the derivatives of f(x) and then using the formula I get f(x) = 1-x+x3.

So I was wondering if
1) Which way is correct
2) is the second one accurate.

Thanks
-James
 
Physics news on Phys.org
  • #2
The second way is accurate. The first way would be as well if you do what they want you to. You are supposed to divide 1 by 1+x+x^2 using polynomial division. The result is NOT 1+x+x^2.
 

Related to Solve Maclaurin Series for f(x)= 1/(1+x+X2)

1. What is a Maclaurin series?

A Maclaurin series is a type of mathematical series that represents a function as an infinite sum of terms. It is named after Scottish mathematician Colin Maclaurin and is a special case of Taylor series where the series is centered at x=0.

2. How do you solve for a Maclaurin series?

To solve for a Maclaurin series, you need to use the general formula for Maclaurin series which is f(x) = f(0) + f'(0)x + f''(0)x^2/2! + f'''(0)x^3/3! + ... + f^n(0)x^n/n!, where f(0) is the value of the function at x=0 and f^n(0) represents the nth derivative of the function at x=0.

3. Why is it useful to find the Maclaurin series of a function?

Finding the Maclaurin series of a function can be useful in many ways. It can help us to approximate the value of a function at a specific point, to evaluate integrals and derivatives of the function, and to understand the behavior of the function near the point of expansion.

4. How do you find the Maclaurin series for f(x)= 1/(1+x+X2)?

To find the Maclaurin series for f(x)= 1/(1+x+X2), we first need to rewrite the function as a geometric series by factoring out an x. This gives us f(x)= 1/(1-x^2). Then, we can use the formula for the geometric series to find the Maclaurin series, which is f(x)= 1 + x^2 + x^4 + x^6 + ... = Σ(x^n)^2.

5. What is the significance of the Maclaurin series for f(x)= 1/(1+x+X2)?

The Maclaurin series for f(x)= 1/(1+x+X2) is significant because it represents a rational function as an infinite polynomial. This allows us to easily evaluate the function and its derivatives at any point, making it a useful tool in many mathematical applications.

Similar threads

  • Calculus and Beyond Homework Help
Replies
6
Views
2K
  • Calculus and Beyond Homework Help
Replies
17
Views
1K
  • Calculus and Beyond Homework Help
Replies
10
Views
1K
  • Calculus and Beyond Homework Help
2
Replies
38
Views
3K
  • Calculus and Beyond Homework Help
Replies
3
Views
501
  • Calculus and Beyond Homework Help
Replies
2
Views
1K
  • Calculus and Beyond Homework Help
Replies
6
Views
2K
  • Calculus and Beyond Homework Help
Replies
7
Views
2K
  • Calculus and Beyond Homework Help
Replies
16
Views
3K
  • Calculus and Beyond Homework Help
Replies
1
Views
511
Back
Top