Solving the Epsilon-Delta Problem with Sinusoidal Functions

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Homework Help Overview

The discussion revolves around the limit of the function sin(5x)/x as x approaches 0, specifically focusing on the epsilon-delta definition of limits and the implications of sinusoidal functions in this context.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the limit of sin(5x)/x and its value as x approaches 0, with one participant suggesting a practical method to find a value t that satisfies a specific inequality related to the limit.

Discussion Status

The discussion includes various interpretations of the limit and the conditions under which the inequality holds. Some participants provide guidance on finding a suitable value for t, while others question the assumptions regarding the problem's requirements.

Contextual Notes

There is mention of a trial-and-error approach to finding a suitable t, and a note that the problem may not require finding the largest possible x, which raises questions about the problem's constraints.

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What is the limit of sin(5x)/x as x goes to 0? Taking "A" as that value you want to find x such that |sin(x)/x- A|< 0.01.
 
The limit as sin(5x)/x goes to 0 is 5, right?
 
as a practical matter you may want to find t such that:

|sin(t)/t - 1| < 0.01

then use x = t/5.

finding such a t (and thus x) isn't that hard (i did it by trial-and-error in about 2 minutes), the real trick is showing the inequality holds in the interval (-x,x). unless i am mistaken, the problem doesn't ask you to find the largest possible such x, just one that works.
 

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