• Support PF! Buy your school textbooks, materials and every day products Here!

Bounded Function

  • Thread starter hsd
  • Start date
  • #1
hsd
6
0
(a) Show that the function g(x) =[3 + sin(1/x-2)]/[1 + x^2] is bounded.
This means to find real numbers m; M is an lR such that m ≤ g(x) ≤ M for
all x is an lR (and to show that these inequalities are satisfied!).

(b) Explain why the function:

f(x) = { [x-2] [3 + sin(1/x-2)]/[1 + x^2] , if x ≠ 2,
{ 0 , if x = 2.

is continuous at all x ≠ 2.

(c) Show that the function f(x) in Part (b) is continuous at x = 2. [Hint: Use
Part (a) and the Squeeze Theorem.]
 
Last edited:

Answers and Replies

  • #2
lanedance
Homework Helper
3,304
2
how about considering g(x) = u(x)/v(x) and each of the behaviours of those functions

note that g(x) will get big whenever u(x)>>v(x)
 
  • #3
Simon Bridge
Science Advisor
Homework Helper
17,848
1,645
Welcome to PF;
How about showing us your attempt at the problem? ... that way we can target our assistance to where you need it most.
 

Related Threads on Bounded Function

  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
9
Views
2K
Replies
2
Views
5K
  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
3
Views
4K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
1
Views
990
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
2
Views
4K
Top