Trig Limits: Does x/sin(x) = 1 as x-->0?

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Homework Help Overview

The discussion revolves around the limit of the function x/sin(x) as x approaches 0, exploring its relationship to the limit of sin(x)/x, which is known to equal 1.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the manipulation of the limit expressions and question how the relationship between sin(x) and x can be used to derive the limit of x/sin(x).

Discussion Status

Some participants have provided insights into the manipulation of the limits, suggesting that understanding the reciprocal relationship between the two limits could clarify the concept. However, the discussion does not reach a consensus on the implications of these manipulations.

Contextual Notes

The original poster notes that this inquiry is more of a reflective thought rather than a formal homework question, indicating a casual exploration of the topic.

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This isn't really a homework question--but just something I was thinking about while doing homework.

Since lim(sinx/x) as x--->0 = 1

does that mean that lim(x/sinx) as x--->0 = 1 ?
 
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yes, you can manipulate the x/sinx to sinx/x which will give you 1
 
cool, how is that done?
 
lim x/sinx = lim 1/(sinx/x) = 1/1 = 1
as x->0
 
oh wow, that waas a long time ago, forgot about that :o

haha, thank
 

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