Continuity, proving that sin(x)sin(1/x) is continuous at 0.

  • #1

Homework Statement



Define f(x)=sin(x)sin(1/x) if x does not =0, and 0 when x=0.

Have to prove that f(x) is continuous at 0.

Homework Equations



We can use the definition of continuity to prove this, I believe.



The Attempt at a Solution



I know from previous homework assignments that sin(x) is continuous at 0, but sin(1/x) is not. Is there a way I can use this knowledge to help me solve this problem, or do I need to start from scratch? If I need to start from scratch, do I apply the definition of continuity?
 

Answers and Replies

  • #2
phyzguy
Science Advisor
4,949
1,888
Apply the definition of continuity, and think about what these functions do as they approach zero. While sin(1/x) oscillates wildly, it remains bounded. So what is the limit of your function as x->0?
 

Related Threads on Continuity, proving that sin(x)sin(1/x) is continuous at 0.

  • Last Post
Replies
12
Views
17K
Replies
1
Views
2K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
2
Views
7K
Replies
15
Views
23K
  • Last Post
Replies
4
Views
7K
  • Last Post
Replies
2
Views
43K
  • Last Post
Replies
9
Views
14K
Top