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

Limits of Trigonometric Functions. !

  • Thread starter gabyoh23
  • Start date
  • #1
6
0
Limits of Trigonometric Functions. URGENT!

Homework Statement


Evaluate stackrel{lim}{x [tex]\rightarrow[/tex]0}[/tex] [sin(\frac{2e}{x3}) \bullet (arctanx)]


Homework Equations


All I know is that the equation stackrel{lim}{x [tex]\rightarrow[/tex]0}[/tex] [tex]\frac{sin x}{x}[/tex] = 1 might be helpful, but I'm not sure how to apply it to this particular problem.


The Attempt at a Solution


I talked to a friend of mine who's in Calc III, and she said that the whole limit would be equal to 0 since arctan(0) = 0, and sin[tex]\frac{2e}{x3}[/tex] is undefined, and the zero beats out the undefined value. This might be right, but how would I show that mathematically?

All help is greatly appreciated as I'm kind of in a crunch here :)
 

Answers and Replies

  • #2
33,635
5,295


Homework Statement


Evaluate stackrel{lim}{x [tex]\rightarrow[/tex]0}[/tex] [sin(\frac{2e}{x3}) \bullet (arctanx)]


Homework Equations


All I know is that the equation stackrel{lim}{x [tex]\rightarrow[/tex]0}[/tex] [tex]\frac{sin x}{x}[/tex] = 1 might be helpful, but I'm not sure how to apply it to this particular problem.


The Attempt at a Solution


I talked to a friend of mine who's in Calc III, and she said that the whole limit would be equal to 0 since arctan(0) = 0, and sin[tex]\frac{2e}{x3}[/tex] is undefined, and the zero beats out the undefined value. This might be right, but how would I show that mathematically?

All help is greatly appreciated as I'm kind of in a crunch here :)
Here's your corrected limit expression.

Evaluate [tex]lim_{x \rightarrow 0} sin(\frac{2e}{x^3}) arctanx[/tex]

Your friend is leading you astray. It's not necessarily true that an expression tending to zero "beats out" an undefined value. What is true is that -1 <= sin(u) <= 1 for all real values of u.
 
  • #3
6
0


Thanks for correcting my formatting. I was in a rush, and I accidentally hit the "submit post" button before previewing it.

Thanks for the input!!
 

Related Threads on Limits of Trigonometric Functions. !

  • Last Post
Replies
9
Views
4K
  • Last Post
Replies
4
Views
798
  • Last Post
Replies
4
Views
1K
  • Last Post
3
Replies
54
Views
3K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
7
Views
15K
Replies
7
Views
2K
  • Last Post
Replies
4
Views
1K
Replies
3
Views
2K
  • Last Post
Replies
2
Views
2K
Top