We have observed that we cannot use direct substitution or the quotient law to find the limit$.$ We can now attempt to simplify the given function before evaluating the limit to see if that works.

We note that if we expand the numerator and then factor it$,$ the resulting rational expression can be simplified as follows.

$($h $7)249$h

$=$

h$2$

$$h $+4949$h

$$

$=$

h$2$

$$hh

$=$

h$$

h $$

h

$$

$=$h $$

Note that it is valid to cancel the common factor h from the numerator and denominator because

h $0$

for the values the function is evaluated at for the limit$.$ The variable h approaches $0$ but is not equal to $0.$