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

Squeeze Theorem

  • Thread starter zeroheero
  • Start date
2
0
Hi, I have an assignment question that asks if f(x) = x^2sin(pi/x), prove that f(0) can be defined in such a way the f becomes continuous at x = 0.
Am I able to apply the squeeze theorem to show,
-1<sin(pi/x)<1
add x^2 to the inequality
-x\<x^2sin(pi/x)\<x^2. (\< us less than or equal to)
Lim as x approaches 0 from the left side, -x^2=0; and
Lim as x approaches 0 from the right side, x^2=0
if g(x) =-x^2 F(x) = x^2sin(pi/x). h(x)= x^2

Is this the best way tom get about this question?
 
Pretty much. It is the easiest way without invoking other theorems.
 

Related Threads for: Squeeze Theorem

  • Posted
Replies
17
Views
4K
  • Posted
Replies
2
Views
621
  • Posted
Replies
7
Views
1K
  • Posted
Replies
4
Views
3K
  • Posted
Replies
3
Views
1K
  • Posted
Replies
5
Views
532
  • Posted
Replies
4
Views
3K
  • Posted
Replies
5
Views
870

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top