Limit w/Tangent: Solve & Discuss

  • Thread starter Thread starter dobry_den
  • Start date Start date
  • Tags Tags
    Limit Tangent
dobry_den
Messages
113
Reaction score
0

Homework Statement



Solve the following limit:

\lim_{x \rightarrow 1}(1-x)\tan{\left(\frac{\pi x}{2}\right)}

The Attempt at a Solution



I solved it using L'Hospital rule, it's equal to 2/pi, but is there any other way how to solve it? thanks a lot!

The same question would apply to

\lim_{x \rightarrow \frac{\pi}{3}}\left(\frac{\sin{\left(x-\frac{\pi}{3}\right)}}{1-2\cos{x}}\right)
 
Last edited:
Physics news on Phys.org
Well, I've finally found a different way how to solve it... I post it here since it can be useful to someone..

I substituted x with y = x-1, and then after some steps I've arrived at the following limit:

\lim_{y \rightarrow 0}\frac{\frac{\pi}{2}y}{\sin{\frac{\pi}{2}y}}\frac{2}{\pi}\cos{\frac{\pi}{2}y} = \frac{2}{\pi}
 
Thread 'Use greedy vertex coloring algorithm to prove the upper bound of χ'
Hi! I am struggling with the exercise I mentioned under "Homework statement". The exercise is about a specific "greedy vertex coloring algorithm". One definition (which matches what my book uses) can be found here: https://people.cs.uchicago.edu/~laci/HANDOUTS/greedycoloring.pdf Here is also a screenshot of the relevant parts of the linked PDF, i.e. the def. of the algorithm: Sadly I don't have much to show as far as a solution attempt goes, as I am stuck on how to proceed. I thought...
Back
Top