Limit Q: Lim as x->infinity of Sin(pie-x)/(pie-x)

[Guest]

I have this question i cant start it or figure it out, can some one help me?

Lim as x->infinity of Sin(pie-x)/(pie-x)

The answer is one and i dont know how.

Thanks

 

[tkhunny]

1) "pie" is for eating. "pi" is for math.
2) What tools have we with which to work?

Have you considered expanding the sine of the difference into sine and cosine? You probably don't want to do that.

Have you considered that -1 <= sin(x) <= 1 fox x in the Reals? That should lead you somewhere.

 

[Guest]

i was going to put pi but then i thought poeple will get confused, sorry. The -1 thing, what do you mean?

 

[soroban]

Re: Limit question

Hello, adon!

Is there a typo?
As written, the limit is zero.

Could the limit be: \(\displaystyle x\to\pi\) ?

\(\displaystyle \L\lim_{x\to\pi}\frac{\sin(\pi\,-\,x)}{\pi\,-\,x}\) has a limit of \(\displaystyle 1.\)