Analysis Homework Help

In summary, the conversation discusses the relationship between differentiable functions f and g on the real numbers, and their derivatives. It is shown that if f'(x) is always less than or equal to g'(x) for all x greater than or equal to a, then f(x) will also be less than or equal to g(x) for all x greater than or equal to a. This result has a physical interpretation. Additionally, using the Mean Value Theorem, it is proven that if a differentiable function's derivative is bounded, then the function itself is uniformly continuous. On the other hand, if the limit as x approaches infinity of the derivative is infinity, then the function cannot be uniformly continuous. Lastly, an example is given
  • #1
429
2

Homework Statement


Suppose f and g are differentiable on R, and f(a) = g(a) and f'(x) <= g'(x) for all x >= a. Show that f(x) <= g(x) for all x >= a. Give a physical interpretation of this result.

Also, using the Mean Value Theorem:
(a) Let f: R --> R be a differentiable function. Suppose that its derivative f'(x) is bounded Prove that f is uniformly continuous.
(b) Let f: R --> R be a differentiable function. Suppose that lim (x --> infinity) f'(x) = infinity. Show that f cannot be uniformly continuous.
(c) Let g(x) = (x)^1/2 show that g'(x) is unbounded on (0,1] but g(x) is uniformly continuous on [0,1].

Homework Equations





The Attempt at a Solution


I don't know how to quite formulate the inequalities, any help?
 
Physics news on Phys.org
  • #2
Consider the function f-g.
 
  • #3
i still don't see it, any more hints? thanks
 
  • #4
(f-g)(a) = 0, (f-g)'(x) < 0 for all x > a. Use MVT to prove that (f-g)(x) < 0 for all x > a.
 

What is analysis homework help?

Analysis homework help is a service that provides assistance to students who are struggling with their analysis assignments. This can include guidance on understanding concepts, completing calculations, and writing reports or essays.

Why do students seek analysis homework help?

There are several reasons why students may need analysis homework help. Some students may find the subject challenging and need extra support to fully understand the material. Others may struggle with time management and need help completing their assignments on time. Additionally, some students may need help with specific topics or concepts that they find particularly difficult.

What kind of assignments can be helped with?

Analysis homework help can assist with a variety of assignments, including problem sets, lab reports, research papers, case studies, and more. The service is designed to help students with any kind of analysis-related assignment they may encounter in their coursework.

Who provides analysis homework help?

Analysis homework help is typically provided by experienced tutors or professionals in the field of analysis. These individuals have a strong understanding of the subject matter and can provide students with personalized and effective guidance to improve their understanding and performance in their assignments.

How can students access analysis homework help?

Students can access analysis homework help through a variety of resources, such as online tutoring services, academic support centers, study groups, and even through their professors or classmates. It is important for students to take advantage of these resources and seek help when needed to improve their understanding and performance in their analysis assignments.

Suggested for: Analysis Homework Help

Replies
7
Views
919
Replies
2
Views
679
Replies
2
Views
670
Replies
1
Views
590
Replies
13
Views
2K
Replies
1
Views
641
Back
Top