Find $ \lim _{y \rightarrow 0} \frac{\sqrt{15+y}-\sqrt{15}}{y} $.
A) $ \frac{\sqrt{15}}{30} $
B) $ \frac{\sqrt{15}}{15} $
C) 0
D) $ \frac{\sqrt{15}}{2} $
E) limit does not exist

Question

Quizplus · Accepted Answer

Using the difference of squares formula, we have$$\lim _{y \rightarrow 0} \frac{\sqrt{15+y}-\sqrt{15}}{y}=\lim _{y \rightarrow 0} \frac{(\sqrt{15+y}-\sqrt{15})(\sqrt{15+y}+\sqrt{15})}{y(\sqrt{15+y}+\sqrt{15})}$$$$=\lim _{y \rightarrow 0} \frac{15+y-15}{y(\sqrt{15+y}+\sqrt{15})}$$$$=\lim _{y \rightarrow 0} \frac{y}{y(\sqrt{15+y}+\sqrt{15})}$$$$=\lim _{y \rightarrow 0} \frac{1}{\sqrt{15+y}+\sqrt{15}}$$$$=\frac{1}{\sqrt{15}+\sqrt{15}}=\frac{1}{2\sqrt{15}}=\frac{\sqrt{15}}{30}$$

Find lim⁡y→015+y−15y \lim _{y \rightarrow 0} \frac{\sqrt{15+y}-\sqrt{15}}{y} limy→0​y15+y​−15​​ A) 1530 \frac{\sqrt{15}}{30} 3015​​

Find $\lim _{y \rightarrow 0} \frac{\sqrt{15+y}-\sqrt{15}}{y}$
A) $\frac{\sqrt{15}}{30}$