# Thread: use continuity to evaluate the limit

1. ## use continuity to evaluate the limit

$\displaystyle \lim_{x\to4}$ (5+sqrt(x))/(sqrt(5)+x)

Answer is 7/3 but i have no idea how to get that answer. I tried but i get something else

2. Originally Posted by yoman360
$\displaystyle \lim_{x\to4}$ (5+sqrt(x))/(sqrt(5)+x)

Answer is 7/3 but i have no idea how to get that answer. I tried but i get something else
personally, i think there should be a typing error.
it should be $\displaystyle \lim_{x\to4}\frac{(5+\sqrt{x})}{(\sqrt{5+x})}$
not $\displaystyle \lim_{x\to4}\frac{(5+\sqrt{x})}{(\sqrt{5}+x)}$

3. Originally Posted by ynj
personally, i think there should be a typing error.
it should be $\displaystyle \lim_{x\to4}\frac{(5+\sqrt{x})}{(\sqrt{5+x})}$
not $\displaystyle \lim_{x\to4}\frac{(5+\sqrt{x})}{(\sqrt{5}+x)}$
ur correct i wrote it incorrectly

4. then$\displaystyle \lim_{x\to4}\frac{(5+\sqrt{x})}{(\sqrt{5+x})}=\fra c{\lim_{x\to4}(5+\sqrt{x})}{\lim_{x\to4}(\sqrt{5+x })}=\frac{7}{3}$