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

[hpthinker]

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.

 

[╔(σ_σ)╝]

Are you familiar with the following limit ?

$$\lim_{x \to 0} \frac{sin \left( x \right)}{x} = 1$$

 

[hpthinker]

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$$\pi$$ ?

 

[╔(σ_σ)╝]

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 $$\lim_{t \to 0} \frac{ sin(5(t- \pi))}{t} = \lim_{t \to 0} \frac{-sin(5t)}{t}$$