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.
$$ \lim_{x\to0} \frac{5-\sqrt{x+25}}{x}$$
Could someone give me a hint as to what I need to do to the fraction to make this work? Thanks!
Answer
$$\lim_{x\to0} \frac{5-\sqrt{x+25}}{x}=\lim_{x\to0} \frac{(5-\sqrt{x+25)}(5+\sqrt{x+25})}{x(5+\sqrt{x+25})}=\lim_{x\to0} \frac{25-(x+25)}{x(5+\sqrt{x+25})}=-\frac{1}{10}$$
No comments:
Post a Comment