Friday, 26 September 2014

real analysis - Proving a set is compact!

This is the last one i need help with and the help is much appreciate as I seem to have found myself stuck and pretty much turned in a blank worksheet to my professor. He says these types of problems will be on our final, and I have no clue where to start.




Suppose I claim that the set {(x,y) $\in$ $\Bbb R^2$ : $e^x + e^y \le 100$ and x+y $\ge 0 $} is compact. Prove this while also stating the theorems needed in obtaining the proof. I also think it would be helpful if anyone can verify why the hypotheses are satisfied if it isn't any bother...

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real analysis - How to find $lim_{hrightarrow 0}frac{sin(ha)}{h}$

How to find $\lim_{h\rightarrow 0}\frac{\sin(ha)}{h}$ without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...