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題目如下, 請高手幫幫忙 ^^+ i" s" d+ @% k
1. Write a function that as input has an expression f, and returns the logarithmic derivate 1/f (d f)/(d x) . Use a conditional or pattern test to make your function accept any symbols as input except for lists.
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" g2 X6 F: W# La) Write a recursive function that computes the function f[n] defined by 6 n f[n]=f[n-1]+n! for n>0, and f[0]=7. Restrict the argument to positive integers.
$ J8 K" a3 }5 L! n, ?) ~2 [2 |b) Write and test a program that computes f[n] using Module and a While loop.
0 B$ v/ U( X+ |9 V' b4 Jc) Compare the timings of the two methods by computing f[n] in both cases for very large values of n and/or doing the computation many times. You may have to use Clear or restart to clear Mathematica's memory of previous calculations. Explain your results.
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$ V# ]6 a4 W: @3 F1 G9 RConsider the iterative map Subscript[x, n] == 1/2 Subsuperscript[x, n-1, 2] -\[Mu]. , }6 j) c* ]) o: @# n% a) p
a) Compute its fixed points and 2-cycles as a function of \[Mu].
( ^" ]" i- p9 `. v$ l8 v9 Nb) Using linear stability analysis, compute the range of stability of both the fixed points as well as the 2-cycles. & b9 g/ w8 x. }/ l( ~0 i. o1 w: H
c) Show cobweb diagrams for representative parameters illustrating the (un)stable fixed point and 2-cycle. 4 |0 m7 I* ?+ B, U/ Y1 k
d) Graphically demonstrate the onset of a stable 3-cycle.
% @7 n2 Y6 A$ ^; _1 fe) Produce the bifurcation diagram. |
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