Trig Limit question

  • Thread starter helpcalc
  • Start date
  • #1
4
0
Could someone help me with this one. My teacher says I'm wrong when I solved this limit as undefined. thanks!

lim as x goes to zero of (sin x tan x -1)/4x
 

Answers and Replies

  • #2
867
0
If you mean (sin(x)tan(x)-1)/(4x), then it would be undefined. I have a feeling that the -1 is causing a problem since you may be missing parentheses that would change the problem and let a limit exist.
 
  • #3
537
3
If the limit you are asking about is
[tex]\lim_{x\to 0} \frac{\sin x \tan x - 1}{4x}[/tex]
then the limit is undefined, and your teacher is wrong. The way to determine this is to look at the limit as x approaches 0 from the left and then from the right.

The limit of the numerator as x approaches 0 is -1. As x approaches 0 from the left, x is negative and so the limit will be positive infinity. As x approaches 0 from the right, x is positive, so you will get negative infinity. Therefore, the limit does not exist since the left and right handed limits aren't equal.
 
  • #4
4
0
thanks for the responses but when i graph this function at 0 the function is zero. It looks like it is continuous and goes to zero from the left and right but i can't find a mathematical way to solve it.
 
  • #5
Cyosis
Homework Helper
1,495
0
Well you must have drawn the graph incorrectly. For example what value did you get for x=0.1 and x=-0.1?
 
  • #6
4
0
for -.01 the limit is .0025 and for .01 the limit is -.0025. looking at a graphing calculator using the table function, it looks like it converges to 0.
 
  • #7
Cyosis
Homework Helper
1,495
0
I see, that means we're talking about different functions and so are the other posters in this thread.

The limits you describe correspond with the function:

[tex]
x \left(\frac{\sin x \tan x -1}{4}\right)
[/tex]

We assumed you meant:

[tex]
\frac{\sin x \tan x - 1}{4x}
[/tex]

Could you clarify which one it is?
 
  • #8
4
0
my mistake on the calculator. it is definitely the second one. looking at the graph my teacher must be wrong (I hope!!!!!!) thanks for your help!!!!!!!!!
 
  • #9
Cyosis
Homework Helper
1,495
0
If it's the second one then the limit does not exist.
 

Related Threads on Trig Limit question

  • Last Post
Replies
10
Views
2K
  • Last Post
Replies
3
Views
873
  • Last Post
Replies
5
Views
5K
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
10
Views
3K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
1
Views
889
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
5
Views
1K
Top