Evaluate the limit as x turns to 0
Lim [√(5+x) - √5 / x]
limx→05+x−5x=limx→0(5+x−5)(5+x+5)x(5+x+5)=lim_{x\to 0}\frac{\sqrt{5+x}-\sqrt{5}}{x}=lim_{x\to 0}\frac{(\sqrt{5+x}-\sqrt{5})(\sqrt{5+x}+\sqrt{5})}{x(\sqrt{5+x}+\sqrt{5})}=limx→0x5+x−5=limx→0x(5+x+5)(5+x−5)(5+x+5)=
=limx→0xx(5+x+5)=limx→015+x+5=125.=lim_{x\to 0}\frac{x}{x(\sqrt{5+x}+\sqrt{5})}=lim_{x\to 0}\frac{1}{\sqrt{5+x}+\sqrt{5}}=\frac{1}{2\sqrt{5}}.=limx→0x(5+x+5)x=limx→05+x+51=251.
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