Question about Maclaurin series - calculus

That's all.In summary, the conversation discusses finding the Maclaurin series of a given function and determining the coefficients for different powers of x. The attempt at a solution results in the correct coefficient for c_3 but an incorrect one for c_5, which is later clarified to be c_5 instead of c_4. It is noted that the answer given may have used a different denominator for the coefficient, resulting in a seemingly different answer.
  • #1
andydan1060
2
0

Homework Statement


Find the Maclaurin series of the function https://webwork.wustl.edu/webwork2_files/tmp/equations/87/63afd4b6f3566e2a90aa420dc5d1821.png
c_3 =
c_4 =
c_5 =
c_6 =
c_7 =

Homework Equations


upload_2015-4-27_0-43-19.png


The Attempt at a Solution


(8x^2)[(9x) - (9x)^3/3! + (9x)^5/5! - (9x)^7/7! + ...]

I got c_3 = 72, which is correct, and c_5 = (8x^2)[(9x^3)/3!] = 5832/3! (coefficient)

Apparently that's wrong and it's supposed to be -116640/(5!).

What did I do wrong? Thanks!
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
Are you not just muddling up which coefficient is which? If you've got 1/3! and the answer has 1/5! then those are different coefficients.
 
  • #3
Isnt c4 supposed to be the coefficient of x^4 which is zero in this series?
 
  • #4
andydan1060 said:

Homework Statement


Find the Maclaurin series of the function https://webwork.wustl.edu/webwork2_files/tmp/equations/87/63afd4b6f3566e2a90aa420dc5d1821.png
c_3 =
Delta² said:
Isnt c4 supposed to be the coefficient of x^4 which is zero in this series?
It's supposed to be
c_4 =
c_5 =
c_6 =
c_7 =

Homework Equations


View attachment 82633

The Attempt at a Solution


(8x^2)[(9x) - (9x)^3/3! + (9x)^5/5! - (9x)^7/7! + ...]

I got c_3 = 72, which is correct, and c_4 = (8x^2)[(9x^3)/3!] = 5832/3! (coefficient)

Apparently that's wrong and it's supposed to be -116640/(5!).

What did I do wrong? Thanks!
Delta² said:
Isnt c4 supposed to be the coefficient of x^4 which is zero in this series?
It's supposed to be c_5, not c_4, sorry.
 
Last edited by a moderator:
  • #5
andydan1060 said:
It's supposed to be c_5, not c_4, sorry.

First, your coefficient should have a minus.

Second, why do you think your answer and the answer given are different? Just because they look different doesn't mean they are!
 
  • Like
Likes Delta2
  • #6
Well PeroK is right, doing the calculations it turns out that 5832/3!=116640/5!. However i wonder if your teacher wanted you to do this assignment by manually calculating up to the 7th derivative of 8x^2sin(9x) and evaluating the derivatives at 0.
 
  • #7
Delta² said:
Well PeroK is right, doing the calculations it turns out that 5832/3!=116640/5!. However i wonder if your teacher wanted you to do this assignment by manually calculating up to the 7th derivative of 8x^2sin(9x) and evaluating the derivatives at 0.

I suspect that since we have the coefficient of ##x^5##, whoever gave the answer preferred to have ##5!## in the denominator.
 

What is a Maclaurin series?

A Maclaurin series is a type of power series expansion that represents a function as an infinite sum of powers of the independent variable, centered at 0. It is named after the Scottish mathematician Colin Maclaurin.

What is the purpose of using a Maclaurin series in calculus?

Maclaurin series are useful in calculus because they allow us to approximate complicated functions with simpler ones, making it easier to perform calculations and analyze the behavior of the function. They can also be used to find derivatives and integrals of functions.

How do you find the Maclaurin series of a function?

To find the Maclaurin series of a function, we use the Taylor series formula, which involves taking derivatives of the function at 0 and evaluating them at 0. The coefficients of the resulting series are then determined by dividing each derivative by the corresponding factorial.

What is the difference between a Maclaurin series and a Taylor series?

A Maclaurin series is a special case of a Taylor series, where the series is centered at 0. In general, a Taylor series can be centered at any point, while a Maclaurin series is only centered at 0.

What is the interval of convergence for a Maclaurin series?

The interval of convergence for a Maclaurin series is the range of values of the independent variable for which the series converges and accurately represents the original function. This interval can be found by using the ratio test, which involves taking the limit of the absolute value of the ratio of consecutive terms in the series.

Similar threads

Taylor Series of cos(3x^2)
    • Calculus and Beyond Homework Help
Replies
1
Views
3K
Question about deriving Maclaurin Series
    • Calculus and Beyond Homework Help
Replies
8
Views
2K
Correcting Maclaurin Series Coefficient of x^4 | Homework Help
    • Calculus and Beyond Homework Help
Replies
5
Views
1K
Finding the Maclaurin Series Expansion of (1+x)ln(1+x)
    • Calculus and Beyond Homework Help
Replies
12
Views
2K
Simple? maclaurin series (1-x)^-2
    • Calculus and Beyond Homework Help
Replies
3
Views
2K
What is the Relationship Between Maclaurin Series and Infinite Series?
    • Calculus and Beyond Homework Help
Replies
23
Views
2K
Help with Taylor Series/Maclaurin Series Question
    • Calculus and Beyond Homework Help
Replies
15
Views
2K
Deriving Maclaurin series for tanx
    • Calculus and Beyond Homework Help
Replies
7
Views
21K
Help with Maclaurin series of (1/x), (1/x^2), etc
    • Calculus and Beyond Homework Help
Replies
6
Views
3K
Find the Maclaurin Series for tanx
    • Calculus and Beyond Homework Help
Replies
10
Views
26K

Hot Threads

Recent Insights

Back
Top