Limits and Differentiation

                                 Mathematica

Dr. Andrzej Korzeniowski
Department of Mathematics, UTA

Lesson 2

Functions and Limits

Before defining new functions (or re-using previously  used names of  variables) one needs to clear them.

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To evaluate f [x] starting at x = a, ending at x = b with increment dx, use Table[{x, f [x]},{x, a, b, dx}] // TableForm.

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0.5` 0.958851077208406`
0.45` 0.9665900758027339`
0.4` 0.9735458557716263`
0.35` 0.9797080213012895`
0.3` 0.9850673555377986`
0.25` 0.9896158370180917`
0.19999999999999996` 0.993346653975306`
0.14999999999999997` 0.9962542164906615`
0.09999999999999998` 0.9983341664682814`
0.05` 0.9995833854135666`

Below are the one-sided limits of the function [Graphics:Images/lesson2_gr_16.gif] at point x = 2

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The remedy  is to load a package that evaluates the limit  numerically.

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Differentiation

There are several ways  to accomplish differentiation.

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How  to graph  f(x)  together with the tangent line to f(x)  at x = a  is  shown in the example below.

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Converted by Mathematica      March 27, 2001