Question

Exercitiu de la admitere fmi 2013

Answer 1

$l = \lim\limits_{x\to 0}\dfrac{1-\sqrt{1-x+x^2}}{x} \overset{\frac{0}{0}(L'H)}{=} \lim\limits_{x\to 0}\dfrac{\Big(1-\sqrt{1-x+x^2}\Big)'}{x'} = \\ \\ = \lim\limits_{x\to 0}-\dfrac{\dfrac{2x-1}{2\sqrt{1-x+x^2}}}{1}= -\dfrac{-1}{2} = \boxed{\dfrac{1}{2}}$