Do Basic Calculus with Mathematica

Limits

You can calculate this limit function of an expression as x -> Infinity.

You can use the Limit function to test the following definition of a derivative.

You can also specify the direction from which the limit is calculated. The following examples use the Direction option when determining the limit of tan(x).

Computing Derivatives

Using the D command, Mathematica calculates derivatives.

In this example, D is used to find the second derivative in terms of t; hence {t, 2} as the second argument of D.

Computing Integrals

One of the most unique and most powerful aspects of Mathematica is its ability to integrate functions not only numerically but also symbolically. In this first example, we integrate an algebraic expression.

Here, Mathematica calculates the area beneath the curve as defined by the interval from 0 to 3.

Some integrals cannot be done symbolically.

There is no symbolic solution for the following definite integral. However, NIntegrate returns a numerical approximation of the integral in question.