This is Section $2\mathrm{.}3$ Problem $12$:

For the function

f$($x$)=2$

:

$($a$)$ A simplified form of the difference quotient

f$($x$+$h$)$f$($x$)$h

$,$ when

h$0$

$,$ is $.$

$($b$)$ Use the simplified form to compute the difference quotient for the following.

When

x$=2$

and

h$=1$

$,$ the difference quotient is $.$

When

x$=2$

and

h$=0\mathrm{.}2$

$,$ the difference quotient is $.$

When

x$=2$

and

h$=0\mathrm{.}1$

$,$ the difference quotient is $.$

When

x$=2$

and

h$=0\mathrm{.}01$

$,$ the difference quotient is $.$