Find the vertical asymptotes of the graph of the function

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Homework Help Overview

The discussion revolves around identifying the vertical asymptotes of the function tan(x)/x, with a focus on the implications of the function's behavior at specific points, particularly x = 0.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to confirm their understanding of vertical asymptotes, suggesting x = (π(2n+1))/2 as potential asymptotes. Other participants question the absence of a vertical asymptote at x = 0 and explore the reasoning behind this observation.

Discussion Status

The discussion includes attempts to clarify the conditions under which vertical asymptotes occur, with some participants affirming the original poster's assertion while others seek to understand the specific case of x = 0. There is an exchange of confirmations regarding the correctness of the original poster's answer.

Contextual Notes

Participants are navigating the implications of limits and the behavior of the function at critical points, particularly in relation to the definition of vertical asymptotes.

Barbados_Slim
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Homework Statement


Find the vertical asymptotes of the graph of the function. (Use n as an arbitrary integer)
\frac{tanx}{x}


Homework Equations


N/A


The Attempt at a Solution


I believe the answer is x=\frac{\pi(2n+1)}{2}. I would just like somebody to confirm or deny this. Thanks in advance.
 
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If you are right, why is there no vert. asymptote at x = 0 ?
 
Is it because the limit as x approaches 0 is 1?
 
Correct !

So your answer in post #1 of this thread is right !
 
Thank you for your help.
 

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