Saturday, 28 December 2013

calculus - Solving limit without L'Hôpital



I need to solve this limit without L'Hôpital's rule. These questions always seem to have some algebraic trick which I just can't see this time.



lim



Could someone give me a hint as to what I need to do to the fraction to make this work? Thanks!


Answer



\lim_{x\to0} \frac{5-\sqrt{x+25}}{x}=\lim_{x\to0} \frac{(5-\sqrt{x+25)}(5+\sqrt{x+25})}{x(5+\sqrt{x+25})}=\lim_{x\to0} \frac{25-(x+25)}{x(5+\sqrt{x+25})}=-\frac{1}{10}


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