MHB Can Dividing by Sin x Help Prove Continuity at x = 0?

  • Thread starter Thread starter Joe20
  • Start date Start date
  • Tags Tags
    Continuous Proof
Click For Summary
Dividing by sin x is suggested as a potential method to prove continuity at x = 0. Participants express uncertainty about the appropriateness of the hint provided with the problem. The discussion emphasizes the importance of using sin x in the approach. The conversation revolves around finding a suitable method to tackle the continuity proof. Overall, the focus remains on the mathematical strategy involving sin x.
Joe20
Messages
53
Reaction score
1
Not sure how to do this question. Help needed. Thanks
 

Attachments

  • 3.png
    3.png
    7 KB · Views: 123
Physics news on Phys.org
Another hint:
Use the well-known result $\displaystyle\lim_{x\to0}\frac{\sin x}x=1$.
 
Olinguito said:
Another hint:
Use the well-known result $\displaystyle\lim_{x\to0}\frac{\sin x}x=1$.


Given the hint that comes with the problem, I wouldn't think that would be appropriate. Alternatively one might suggest dividing everything by $\sin x$, which seems more in line with the hint.
 

Thread 'About the definition of topological manifold using closed sets'

We all know the definition of n-dimensional topological manifold uses open sets and homeomorphisms onto the image as open set in ##\mathbb R^n##. It should be possible to reformulate the definition of n-dimensional topological manifold using closed sets on the manifold's topology and on ##\mathbb R^n## ? I'm positive for this. Perhaps the definition of smooth manifold would be problematic, though.
View full post »

Similar threads

Undergrad Proving a function f is continuous given A U B = X
  • · Replies 5 ·
Replies
5
Views
3K
MHB Continuity of f^+ .... Browder Corollary 3.13
  • · Replies 4 ·
Replies
4
Views
2K
MHB Proof that Arcsin x is continuous ....
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Continuity of f^+ .... Browder Corollary 3.13
  • · Replies 18 ·
Replies
18
Views
2K
Graduate Question about existence of path-lifting property
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Understanding an argument in Intermediate Value Theorem
  • · Replies 5 ·
Replies
5
Views
3K
MHB Compactness and Continuity in R^n .... .... D&K Theorem 1.8.8 .... ....
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Definitions of Continuity in Topological Spaces ....
  • · Replies 2 ·
Replies
2
Views
3K
MHB Piecewise function: differentiable but not continuously differentiable
  • · Replies 21 ·
Replies
21
Views
2K
MHB Composition of Two Continuous Functions .... Browder, Proposition 3.12 .... ....
  • · Replies 2 ·
Replies
2
Views
2K