Why is cot(x) continious in (0,pi) ?

  • Thread starter phymatter
  • Start date
  • #1
131
0
why is cot(x) continious in (0,pi) ???

why is cot(x) continious in (0,pi) ???
I mean Cot(x)=1/Tan(x) , now at pi/2 , tan(x) tends to infinity => 1/tan(x) tends to 0 , now
1/tan(x) is certainly not = 0 , therefore how can cot(x) be continious ?????????
 

Answers and Replies

  • #2
Integral
Staff Emeritus
Science Advisor
Gold Member
7,212
56


So for values near, but less then pi/2, Tan goes to +infinity; for values near, but greater then pi/2, tan goes to -infinity. What does that mean about the continuity of cot?

In a case like this you need to look at the two limits of 1/tan, one coming from the left, the other the right. If they are equal then cot is continuous. In this case both approach zero, so the function is continuous and has the value zero.
 
  • #3
131
0


So for values near, but less then pi/2, Tan goes to +infinity; for values near, but greater then pi/2, tan goes to -infinity. What does that mean about the continuity of cot?

In a case like this you need to look at the two limits of 1/tan, one coming from the left, the other the right. If they are equal then cot is continuous. In this case both approach zero, so the function is continuous and has the value zero.

for a function to be continious at c LHL= RHL at c and also lim at c = f(c) , but here cot(pi/2) does not exist !!
 
  • #4
Integral
Staff Emeritus
Science Advisor
Gold Member
7,212
56


How is it not zero?
 
  • #5
131
0


How is it not zero?


cot(pi/2) only tends to 0 , but is never 0!!!! by defination of limit .
 
  • #6
HallsofIvy
Science Advisor
Homework Helper
41,847
965


No, that does not follow and limits have nothing to do with it. cot(x) is defined as "cos(x)/sin(x)". When x= [itex]\pi/2[/itex], [itex]cos(\pi/2)= 0[/itex] and [itex]sin(\pi/2= 1[/itex] so [itex]cot(\pi/2)= 0[/itex].

You seem to be thinking that cot(x)= 1/tan(x) for all x. It isn't- that is only true as long as both cot(x) and tan(x) exist.
 

Related Threads on Why is cot(x) continious in (0,pi) ?

Replies
6
Views
2K
  • Last Post
Replies
12
Views
1K
  • Last Post
Replies
20
Views
4K
Replies
6
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
16
Views
3K
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
19
Views
1K
  • Last Post
Replies
7
Views
10K
  • Last Post
Replies
4
Views
2K
Top