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Examples - Dæmi

Dæmi:     (styttum burt sameiginlegan þátt)
  1. $\displaystyle \lim_{x\to 1} \frac{x^2 -1}{x-1} = \lim_{x\to 1} \frac{(x+1)(x-1)}{(x-1)} = \lim_{x\to 1} x+1 = 2
$


  2.     $\displaystyle \lim_{x\to 1}\frac{\sqrt{x} - 1}{x-1} = \lim_{x\to 1} \frac{(\sqr...
...{x} + 1)}{(x-1)(\sqrt{x} + 1)} = \lim_{x\to 1} \frac{(x-1)}{(x-1)(\sqrt{x}+ 1)}$  
        $\displaystyle = \lim_{x\to 1} \frac{1}{\sqrt{x} +1} = \frac{1}{2}$  



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