Limits with trigonometric.

[kreshnik]

In the first one I want to know if I can do this:

\(\displaystyle \lim_{x\to1}\;\frac{\text{sin}(1-x)}{x-1}=\lim_{x\to1}\;\frac{\text{sin}(1-x)}{-1(1-x)}=\lim_{x\to1}\;\frac{\text{sin}(1-x)}{1-x}*\frac{1}{-1}=1*(-1)=-1\)

And the second one...

\(\displaystyle $\lim_{x\to\pi}\;\frac{\text{cos}\frac{x}{\pi}}{x-\pi}\)

I have no idea what to do ...

 

[tkhunny]

You appear to have the right idea on the sine.

On the cosine, it appears you just let it scare you. The denominator approaches zero (0), but the numerator is finite and non-zero. x/pi approaches 1, not anything scary.

 

[Deleted member 4993]

.... not anything scary.

But the limit is very scary .... never never land...