Limit (cos(1\x))|tan x| x-> .5pi

  • Thread starter Thread starter rambo123
  • Start date Start date
  • Tags Tags
    Limit
Click For Summary

Homework Help Overview

The discussion revolves around evaluating the limit of the expression (cos(1/x))|tan x| as x approaches π/2. Participants are exploring the behavior of the components of the limit, particularly focusing on the implications of the tangent function as x approaches this value.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • One participant attempts to substitute t = 1/x but expresses difficulty in progressing. Another participant seeks clarification on the limit's approach point, while a third notes that the limit of cos(1/x) exists, prompting a discussion on the behavior of |tan x| as x approaches π/2.

Discussion Status

The discussion is ongoing, with participants raising questions about the limit's approach and the behavior of the functions involved. Some guidance has been offered regarding the existence of the limit for cos(1/x), but there is no explicit consensus on the overall evaluation of the limit.

Contextual Notes

There is a mention of the limit approaching π/2, which may imply specific constraints or considerations regarding the behavior of the tangent function near this value. Participants are also navigating the implications of the infinite nature of |tan x| as x approaches π/2.

rambo123
Messages
2
Reaction score
0

Homework Statement


having a hard time figuring out. I know the answer if infinite but having a hard time proving it

Homework Equations


tan x = cot (.5pi - x) did not help


The Attempt at a Solution


tried substituting t = 1\x got stuck

thanks
 
Physics news on Phys.org
The limit as x goes to what?
 
x goes to (pi)(1\2)

pi 3.14...
 
limx→π/2cos(1/x) exists, so what's left is limx→π/2|tan x|, which is infinite.
 

Similar threads

Replies
3
Views
2K
  • · Replies 12 ·
Replies
12
Views
4K
Replies
5
Views
2K
  • · Replies 9 ·
Replies
9
Views
3K
  • · Replies 19 ·
Replies
19
Views
5K
  • · Replies 4 ·
Replies
4
Views
1K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
1
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 15 ·
Replies
15
Views
2K