Maple supports both differential and integral calculus for a wide range of mathematical expressions. It also easily calculates limits.

For example, we will define an expression
called *sample*:

> sample:=5*x^3-4*x^2+9*x-8; 3 2 sample := 5 x - 4 x + 9 x - 8

Now we will differentiate *sample* with
respect to *x* using the
`diff`

command. The resulting
expression will be stored in
*d_sample*:

> d_sample:=diff(sample,x); 2 d_sample := 15 x -8 x + 9

We can now integrate *d_sample* with
respect to *x*. First off, we shall do
so indefinitely:

> int(d_sample,x); 3 2 5 x - 4 x + 9 x

Now, we shall do so over a specific range of -10 to +10.

> int(d_sample,x=-10..10); 10180

How about another expression,
*sample2*:

> sample2:=(1/(x+exp(x))); 1 sample2 :=---------- x +exp(x)

And when we integrate:

> int(sample2,x=0..2); 2 / | 1 | ----------dx | x + exp(x) / 0

What happened here? Well, Maple was not able
to calculate an exact answer. But a close
approximation of an answer is available with
the `evalf`

command:

> evalf("); .6901755163

Here is another common situation:

> sample3:=1/x; sample3 :=1/x > int(sample3,x); ln(x)

But if we (you know what is coming...) integrate around zero:

> int(sample3,x=0..1); infinity

Maple does not die like most compilers will.

Maple also allows for the calculation of limits.

> sample4:=1/x; sample4 :=1/x > limit(sample4,x=0); undefined > limit(sample4,x=infinity); 0

This page Maintained by Dale H. Leschnitzer

Last Modified Monday, November 4, 1996

**L O S A L A M O S N A T I O N A L L A B O R A T O R Y***Operated by the University of California for the U.S. Department of Energy*