The purpose of this lab is to use Maple to become more familiar with limits of functions, including one-sided limits.

> 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);

- For the function
- State any points where it is undefined.
- Find the limit at .
- If the limit is undefined, show its right and left-handed limits. Then explain why the limit is undefined.
- Plot the function making sure to clearly show the region around the limit point.

- For the function
- State any points where it is undefined.
- Find the limit at .
- If the limit is undefined, show its right and left-handed limits. Then explain why the limit is undefined.
- Plot the function making sure to clearly show the region around the limit point.

- For the function
- State any points where it is undefined.
- Find the limit at .
- If the limit is undefined, show its right and left-handed limits. Then ex plain why the limit is undefined.
- Plot the function making sure to clearly show the region around the limit point.

- For the function

- State any points where it is undefined.
- Find the limit at .
- If the limit is undefined, show its right and left-handed limits. Then explain why the limit is undefined.
- Plot the function making sure to clearly show the region around the limit point.

2008-01-09