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

Limits with trigs

  • Thread starter TommG
  • Start date
  • #1
28
0
I am having trouble solving limits with trig functions.

limx→0 x+xcosx/sinxcosx

useful equation limθ→0 sinθ/θ = 1

my attempt

x+xcosx/sinxcosx

x/sinxcosx + xcosx/sinxcosx

x/sinx*1/cosx + x/sinx this is where I am getting stuck
 

Answers and Replies

  • #2
11,823
5,445
the answer is right in front of you.

As x approaches zero then what is the value of cosx?

and you have the sinx/x as x approaches zero so everything is there for you
 
  • #3
28
0
the answer is right in front of you.

As x approaches zero then what is the value of cosx?

and you have the sinx/x as x approaches zero so everything is there for you

Does x/sinx = 1 also?

I thought sinx had to be in the numerator for it to = 1
 
  • #4
575
76
Does x/sinx = 1 also?

I thought sinx had to be in the numerator for it to = 1
Technically, you're right. But note that if ##x\neq 0##, then ##\frac{x}{\sin x}=\frac{1}{\frac{\sin x}{x}}##, and you have something to which you can apply your limit law for ratios.

So I guess technically you're not right (with regard to the value of the limit), but it's good to be skeptical. I had some students a year or so ago that got marked down (per a grading rubric that was not mine) for omitting the step that I showed.
 

Related Threads on Limits with trigs

  • Last Post
Replies
10
Views
2K
  • Last Post
Replies
4
Views
809
Replies
25
Views
5K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
7
Views
5K
  • Last Post
Replies
8
Views
668
  • Last Post
Replies
5
Views
6K
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
3
Views
834
  • Last Post
Replies
2
Views
593
Top