> limit(x^2+2*x,x=2); > limit(sin(x)/x,x=0); > f := x -> (x+3)/(x^2+7*x+12) ; > limit(f(x),x=-3); > limit(f(x),x=-4);

If the limit exists, Maple can usually
find it. In cases where the limit doesn't exist, Maple gives the
answer `undefined`

or sometimes `infinity`

for an unbounded
limit or gives a range like
`-1..1`

if the limit doesn't exist, but the expression or
function is bounded. See the examples below.

> limit(1/x,x=0); > limit(sin(1/x),x=0);You can also use Maple to compute limits as goes to as shown below.

> f(x); > limit(f(x),x=infinity); > limit(f(x),x=-infinity);

If you want to define your own
piecewise-defined function, then the Maple `piecewise` command
is the best way to do it. Suppose you wanted to define the following
function.

Then the Maple command would be the following.

> g := x -> piecewise(x < 0, -x, x^2+1);If you want to see your function in a more familiar form, just run a command like the one below.

> g(x);The way the

The `limit` command works fine for functions that are defined
via the `piecewise` command, as shown in the example below.

> limit(g(x),x=0); > limit(g(x),x=0,left); > limit(g(x),x=0,right); > plot(g(x), x=-0.1..0.1);

- Use Maple to evaluate each of the limits given below. If the limit exists, state the limit. If the limit does not exist, explain why. A plot may be necessary to support your answer.
- Find the right- and left-hand limits of the following function at
. Also, plot the function and state which piece of the function is used for the right- and left-hand limits.

Does exist? Explain your reasoning. - Consider the following limit.

Use Maple to compute this limit. Is the limit of the difference equal to the difference of the limits? If so, show this is true. If not, explain why the Sum Rule does not apply. You will also need to calculate the two limits seperately.

and

2009-11-04