| Methods / ti-cas.org | |
| Derivation @ the order N |
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Derivation at the order N Derivation of two expressions at the order N. |
Author: Olivier Miclo |
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Public: Students Concepts: real/imag part of a complex num.., recurrence. |
Used material : TI-92 Plus / Voyage 200 |
There is not algorithm making it possible to obtain the derivative at the order N (where N is a symbolic variable) of a function.
The aim of this article is to show how the TI-92 Plus / Voyage 200 can help in the assistance of a such resolution.
I use TI-92 Plus / Voyage 200 for his facility to obtain complex numbers in polar form, his automatic simplification particularly adapted in these examples, and the operator " knowing that " who will be a considerable help.
Example 1: Derivative at the order N of e^x*cos(x)
The idea consists in expressing the function cosine into exponential.
Let us recall that the real part of e^(i*x) is cos(x)
TI-92 Plus / Voyage 200, in mode RECTANGULAR confirms this equality rather easily.
= 
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The first screen shows the work carried out by the function REAL which makes it possible to extract the real part of a complex number. The result is a trigonometrical expression combining sine and cosine. TCOLLECT (development of the trigonometrical expressions) gives us the desired form. |
Here, the operator " knowing that " is very useful. TI-92 Plus / Voyage 200 simplifies 2^2^p into 4^p.
If n=4p,
If n=4p+1, 
If n=4p+2, 
If n=4p+3, 
Example 2: Derivative at the order N of 1/(x²-1)
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and |
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A simple recurrence gives:
and : 
We can thus easily conclude
by: 
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This screen shows the accuracy of the result. |
Olivier Miclo, July 2000
