Limits at infinity of trigometric function

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The limit of sin(x - pi)/(x - pi) as x approaches pi is discussed, with suggestions to apply trigonometric identities and the squeeze theorem. A substitution of u = x - pi is recommended for simplification. Attempts to solve using identities and conjugates did not yield results. The discussion emphasizes the importance of familiar limits in evaluating this expression. Understanding these techniques is crucial for solving limits involving trigonometric functions.
Willian93
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Homework Statement




lim (x→pi)〖sin(x-pi)/(x-pi)〗

Homework Equations



i don't know if we should use trig identity

sin(a-b)= sinA cos B- CosA sin B

The Attempt at a Solution


i use identities to solve that, i did not get the answer. i tried to multiply by conjugate, did not work also.
 
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Think about the squeeze theorem.
 
You could use a substitution, u = x - \pi, and that limit should be familiar.
 

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