Exploring Limits of Trigonometric Functions at x=0

  • Thread starter motorhead87
  • Start date
  • Tags
    Cos Limit
In summary, a limit is the value that a function approaches as the input value approaches a certain value. To find the limit as x approaches 0, you can substitute 0 for x in the function and evaluate the resulting expression. The limit of csc as x approaches 0 does not exist, and the limit of cos as x approaches 0 is 1. A one-sided limit only considers the behavior of a function as the input value approaches the limit from one direction, while a two-sided limit considers the behavior of a function as the input value approaches the limit from both directions.
  • #1
motorhead87
1
0

Homework Statement



lim as x-> 0

(xcsc2x)/(cos5x)


Homework Equations



lim as x-> 0 (sinx)/x = 1


The Attempt at a Solution



(x(1/sin2x)) / (cos5x)

Not sure what I am supposed to do here! Thanks
:)
 
Physics news on Phys.org
  • #2
Firstly, if this is true:

[tex]\lim_{x\rightarrow0} \frac{sin(x)}{x} = 1[/tex]

Then can you figure out what this limit is?

[tex]\lim_{x\rightarrow0} \frac{x}{sin(x)}[/tex]

And then if you use 2x instead of x, this limit should be just as easy:

[tex]\lim_{x\rightarrow0} \frac{2x}{sin(2x)}[/tex]
 

FAQ: Exploring Limits of Trigonometric Functions at x=0

What is the definition of a limit?

A limit is the value that a function approaches as the input value approaches a certain value.

How do you find the limit as x approaches 0?

To find the limit as x approaches 0, you can substitute 0 for x in the function and evaluate the resulting expression.

What is the limit of csc as x approaches 0?

The limit of csc as x approaches 0 does not exist, since the function is undefined at x = 0.

What is the limit of cos as x approaches 0?

The limit of cos as x approaches 0 is 1, since the graph of cos approaches the point (0,1) as x approaches 0.

What is the difference between a one-sided limit and a two-sided limit?

A one-sided limit only considers the behavior of a function as the input value approaches the limit from one direction (either the left or the right). A two-sided limit considers the behavior of a function as the input value approaches the limit from both the left and the right.

Similar threads

Replies
19
Views
2K
Replies
5
Views
1K
Replies
6
Views
1K
Replies
1
Views
2K
Replies
3
Views
2K
Replies
12
Views
1K
Back
Top