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題目如下, 請高手幫幫忙 ^^
% C8 z6 |' v4 V# o1. 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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; Z$ \/ d2 f |7 i0 n/ ^8 ~$ {( Da) 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.
2 q* ^2 z p( @' E/ w9 W- b. d4 pb) Write and test a program that computes f[n] using Module and a While loop.
" \* s' J) y$ o0 hc) 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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Consider the iterative map Subscript[x, n] == 1/2 Subsuperscript[x, n-1, 2] -\[Mu].
) L, c. ^% M" m1 `2 k! ~! Ua) Compute its fixed points and 2-cycles as a function of \[Mu].
8 I6 Q7 e4 A. j: x2 a0 Eb) Using linear stability analysis, compute the range of stability of both the fixed points as well as the 2-cycles. & M; b7 Z: m+ E: m$ E: ~/ H" b
c) Show cobweb diagrams for representative parameters illustrating the (un)stable fixed point and 2-cycle. , v4 ]& Y( y( ] m r' r
d) Graphically demonstrate the onset of a stable 3-cycle.
# ~" _6 `' F) ^' ?$ te) Produce the bifurcation diagram. |
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