> 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.
- Given the following peicewise function:

Plot the function. Does exist? To answer this, you must show that the left and right hand limits agree and are finite. Is the function continuos at ? Explain your reasoning. - Evaluate the following limit.

Next, write the function as the sum of two fucntions, calculate the limits separately and then explain whether or not the limit of the sum is equal to the sum of the limits. (Hint: You will need to calculate each of the following limits:)

2007-10-27