> 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
relate your limits to the graph.

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

Use Maple to compute this limit. Then explain why this does not imply the existence of the two following limits.

and

2006-01-17