EXAMPLE $4$ Evaluate the limit below.

lim$$h $0$

$(5+$ h$)225$h

SOLUTION If we define

F$($h$)=$

$(5+$ h$)225$h

then we can't compute the limit by letting h $=0$ since F$(0)$ is undefined. But if we simplify F$($h$)$ algebraically and simplify at each step, we find that