Finding values of delta that correspond with M=Any Number

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SUMMARY

The discussion centers on finding values of delta that correspond to a limit involving the cotangent function as x approaches 0 from the right, specifically for m=1000 and m=400. Participants emphasize the need for a clear mathematical statement to define the problem, particularly the relationship between delta and m. The correct interpretation involves establishing that if 0 < x < delta, then cot(x) must exceed m. This foundational understanding is crucial for solving the limit problem effectively.

PREREQUISITES
  • Understanding of limits in calculus
  • Familiarity with the cotangent function and its properties
  • Knowledge of epsilon-delta definitions in mathematical analysis
  • Ability to formulate mathematical statements and proofs
NEXT STEPS
  • Study the epsilon-delta definition of limits in calculus
  • Learn about the behavior of the cotangent function near zero
  • Explore examples of limit proofs involving trigonometric functions
  • Practice formulating and solving limit problems with varying values of m
USEFUL FOR

Students studying calculus, particularly those focusing on limits and trigonometric functions, as well as educators seeking to clarify the epsilon-delta approach in mathematical proofs.

realism877
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Homework Statement



For example

you have a limit approaching 0 from the right cot x=infiniti

m=1000



Homework Equations





The Attempt at a Solution

 
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I got as far as this


Cot x=1000

Can someone please help me?
 
realism877 said:

Homework Statement



For example

you have a limit approaching 0 from the right cot x=infiniti

m=1000


realism877 said:
I got as far as this


Cot x=1000

Can someone please help me?


Help you do what? What is the statement of your problem? What does m have to do with it? We aren't mind readers.
 
Cot x= infiniti

As the limit approaches 0 from the right. Find delta that correspond to m=400
 
realism877 said:
Cot x= infiniti

As the limit approaches 0 from the right. Find delta that correspond to m=400

It isn't "the limit approaches 0 from the right". It is x that approaches zero from the right.

To start this problem, the first thing you need to do is state carefully what you are trying to prove. It starts like this:

Given M > 0 we must do what such that what...

State mathematically what you need to prove.
 
I only have to find values of delta that corrspond to m=400.
 
realism877 said:
I only have to find values of delta that corrspond to m=400.

The point is that this means nothing without context- we have absolutely no idea what you are talking about.

However- wild guess- are you trying to find a delta such that 0&lt;x&lt;\delta implies \cot (x) &gt; m ?
 

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