Mastering the MacLaurin Series and Radius of Convergence for f(x) = ln(1-x)

  • Thread starter jkh4
  • Start date
Please do not post duplicate questions.In summary, the conversation discusses the function f(x) = ln(1-x) and its MacLaurin series, radius and interval of convergence, and the Taylor series of its derivative. It also raises the question of whether the Taylor series of f'(x) can be determined without computing the MacLaurin series of f(x) first.
  • #1
jkh4
51
0
Consider the function

f(x) = ln(1-x)

a) compute the MacLaurin series of f(x) (ie: the Taylor series of f(x) around x=0)

b) Compute the radius of convergence and determine the interval of convergence of the series in a)

c) Determine the Taylor series of f'(x) around x=0. Can you do so without using a)?

d) How would you have computed part a) if you had first done part c)?

Thank you!
 
Physics news on Phys.org
  • #2
Hi,

You need to show your work in order to get help. Forum guidelines.
 
  • #3
Someone posted this exact same question in the Calculus and Analysis forum.
 

FAQ: Mastering the MacLaurin Series and Radius of Convergence for f(x) = ln(1-x)

What does it mean to "get started" in science?

Getting started in science means taking the first steps towards conducting research, experimenting, or analyzing data in a specific field of study. It involves identifying a research question, gathering necessary materials or equipment, and formulating a plan to answer the question through the scientific method.

How do I know which research question to pursue?

Choosing a research question can be a challenging but important step in the scientific process. One approach is to start with a topic that interests you and then narrow it down to a specific question. You can also read existing research or talk to experts in the field to identify gaps or unanswered questions that you can explore.

What resources are available to help me get started?

There are many resources available to help you get started in science. These can include books, articles, online databases, scientific journals, and research facilities. You can also seek guidance from mentors, professors, or other professionals in your field of study.

Do I need a specific degree or education to get started in science?

While having a degree in a scientific field can be helpful, it is not always necessary to get started in science. Many researchers and scientists come from diverse educational backgrounds. What is most important is having a curiosity and passion for your chosen field, as well as a willingness to learn and apply scientific methods.

Can I collaborate with other scientists or researchers to get started?

Collaboration is a crucial aspect of science and can be a great way to get started. Working with other scientists or researchers allows you to share ideas, resources, and expertise. You can also learn from one another and potentially produce more impactful research through collaboration.

Similar threads

Show function series involving arctan is not differentiable at x=0
Replies
26
Views
2K
Interval of convergence of power series from ratio test
Replies
2
Views
929
A few questions to make sure I understand Fourier series
Replies
3
Views
1K
Determine Convergence/Divergence of Sequence: f(x)=ln(x)^2/x
Replies
34
Views
3K
Convergence of a Series: Radius and Endpoints
Replies
10
Views
1K
How to show that these sequences are summable?
Replies
1
Views
1K
Taylor/Maclaurin series of a function
Replies
6
Views
2K
Radius of Convergence and Power Series Expansion Around Multiple Values
Replies
6
Views
1K
Power Series and Convergence for ln(x+1)
Replies
22
Views
4K
Finding Maclaurin expansion and interval of convergence
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top