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

To solve this limit, we can use the conjugate method to rationalize the numerator. Multiply the numerator and denominator by the conjugate of the numerator: $\frac{\sqrt{15+y} + \sqrt{15}}{\sqrt{15+y} + \sqrt{15}}$. This simplifies to $\frac{15+y - 15}{y(\sqrt{15+y} + \sqrt{15})}$, which further simplifies to $\frac{1}{\sqrt{15+y} + \sqrt{15}}$. As $y$ approaches 0, this expression becomes $\frac{1}{2\sqrt{15}}$, which is equivalent to $\frac{\sqrt{15}}{30}$.

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

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