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:=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
> 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
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