Mathematics

Problem

For a fixed real number

a>0

, define

g(x)=\frac{\sqrt{a+x}-\sqrt{a}}{x}, \qquad x\ne 0.

Answer the following: a. (i) Evaluate

\displaystyle \lim_{x\to 0} g(x)

in terms of

a

.? b. (ii) Hence, find

\displaystyle \lim_{h\to 0}\frac{\sqrt{9+h}-3}{h}