Limit as X approaches ∞ of (X)(sin(1/X))

  • #1

Homework Statement


lim (x)(sin(1/x))
x->∞

Homework Equations




The Attempt at a Solution


The correct answer is 1, however I do not understand why. I thought that 1/∞ is essentially 0 and sin(0) = 0 so the whole limit would be 0. When I graphed it, the limit did seem to approach 1 though. I don't understand why it doesn't work out algebraically.
 

Answers and Replies

  • #2
UPDATE: wait never mind, i just realized how you can do it algebraically
 
  • #3
35,225
7,043

Homework Statement


lim (x)(sin(1/x))
x->∞

Homework Equations




The Attempt at a Solution


The correct answer is 1, however I do not understand why. I thought that 1/∞ is essentially 0 and sin(0) = 0 so the whole limit would be 0.
No.
You have x becoming unbounded while sin(1/x) is approaching 0. This is the indeterminate form [0 * ∞], meaning that we can't say without taking the limits what will happen.
Michele Nunes said:
When I graphed it, the limit did seem to approach 1 though. I don't understand why it doesn't work out algebraically.
 
  • Like
Likes Michele Nunes
  • #4
No.
You have x becoming unbounded while sin(1/x) is approaching 0. This is the indeterminate form [0 * ∞], meaning that we can't say without taking the limits what will happen.
Ohh, I wasn't aware that 0 * ∞ is considered indeterminate form as well, but that's good to know now though, thank you!
 

Related Threads on Limit as X approaches ∞ of (X)(sin(1/X))

  • Last Post
Replies
3
Views
2K
Replies
15
Views
3K
Replies
9
Views
59K
Replies
2
Views
3K
Replies
7
Views
10K
Replies
2
Views
2K
Replies
13
Views
1K
Replies
2
Views
1K
  • Last Post
Replies
2
Views
43K
  • Last Post
Replies
3
Views
1K
Top