How Do You Solve the Limit of sin(5x)/(x-π) as x Approaches π?

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Homework Help Overview

The discussion revolves around evaluating the limit of sin(5x)/(x-π) as x approaches π. This involves concepts from calculus, specifically limits and trigonometric functions.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the indeterminate form 0/0 encountered when substituting x = π. There is mention of the limit involving sin(x)/x and attempts to manipulate the expression by multiplying by constants. Questions arise about the implications of these manipulations and the correct approach to rewriting the limit.

Discussion Status

The discussion is active, with participants exploring different approaches to the limit. Some guidance has been offered regarding rewriting the limit in terms of a new variable, t, to facilitate evaluation. There is no explicit consensus yet on the best method to proceed.

Contextual Notes

Participants are working under the constraints of a typical homework problem, which may limit the methods they can use or the information they can assume about the functions involved.

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Homework Statement



evaluate the limit: Limit x--> \Pi
sin(5x) / x-\Pi

Homework Equations





The Attempt at a Solution



I get 0/0 since I figure I can't cancel anything out...I think there's another way of solving it I just don't know what way it is...

Thanks for the help.
 
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Are you familiar with the following limit ?

\lim_{x \to 0} \frac{sin \left( x \right)}{x} = 1
 
Last edited:


Yes so if I multiplied top and bottom by 5. I would get 5sin(x) / 5x - 5 \pi wouldn't that give me something like 5/-5\pi ?
 


hpthinker said:
Yes so if I multiplied top and bottom by 5. I would get 5sin(x) / 5x - 5 \pi wouldn't that give me something like 5/-5\pi ?

I misread your question.

Sorry about that.Why don't you do the following t = x - \pi

Your limit becomes \lim_{t \to 0} \frac{ sin(5(t- \pi))}{t} = \lim_{t \to 0} \frac{-sin(5t)}{t}
 
Last edited:

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