Many calculus commands are included in Maple's help menu. A few of these are covered here. Maple allows us to find sums, definite integrals, limits, and first and second derivatives.
sum
To find the sum of an arithmetic series Maple uses the command sum( expression, n = a..b );, where a is the first term and b is the last term. Notice that Maple requires TWO DOTS between the first and last terms rather than the customary mathematical notation of three. The sum of the finite arithmetic series, 4k, from k = 1 to k = 100 can be found as follows.
The formula for the sum of the arithmetic series for 6k from k = 1 to n is
The sum of the finite geometric series for (1/3)^k from k = 1 to k = 10 is
The sum of the infinite geometric series for (1/10)^k from k = 1 to infinity is
int
Values of definite integrals may be computed using the int command. If we want to find the definite integral of f(x) = 1/x from x = 2 to x = 3, we type
Note that like summation, Maple requires TWO DOTS for the limits of integration.
limit
Clearly, as x approaches 1, 2x + 3 approaches 5. To have Maple calculate this limit just type
Another example is
The correct way to read this command is "find the limit of sin(x)/x as x approaches 0". Unfortunatly Maple's syntax invites us to misinterpret the limit process when it uses "x = 0" to mean "as x approaches 0". It would have been better if Maple used "x -> 0". In any case it is up to us to remember this when using the limit command.
Maple can find the limit of many different kinds of functions. To find the limit of e^x as x approaches infinity, we type
Here the limit is taken as x approaches 0 from the left. abs(x) is the absolute value of x.
diff
Maple calculates derivatives of functions using the diff command. We type diff( expression, x );.
The second derivative can be found by typing the diff command twice.
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Jo Norby-Davis: jnorbyda@nmu.edu.