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Derivative chains. (Posted on 2009-03-29) Difficulty: 3 of 5
For any polynomial function f(x) if you know f(a), f'(a), f"(a), f"'(a)... for some value of a you can reconstruct the function. This is true even if the polynomial has an infinite number of terms.

(f' is the first derivative of f, f" is the second derivative etc.)

Define s(a) to be the sequence of f(a), f'(a), f"(a), f"'(a), ...

For each of the following, find the function:

(1) s(1) = 19, 23, 32, 18, 0, 0, 0, 0, ...

(2) s(0) = 1, 2, 4, 8, 16, 32, ...

(3) s(1) = 1, -1, 1/2, -1/6, 1/24, -1/120, 1/720, ...

(4) s(0) = 0, 1, 0, -1, 0, 1, 0, -1, ...

(5) s(0) = ln(2), ln(2ln(2)), ln(2ln(2ln(2) )), ...

No Solution Yet Submitted by Jer    
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Comments: ( You must be logged in to post comments.)
  Subject Author Date
Some Thoughts4 of 5 solvedBrian Smith2016-06-25 22:19:38
re: Keep tryingHarry2009-04-03 00:06:20
Keep tryingJer2009-04-02 13:35:30
re(2): Partially done but help needed (Spoiler)Daniel2009-03-31 21:03:02
re: Partially done but help needed (Spoiler)JayDeeKay2009-03-30 13:30:09
Partially done but help needed (Spoiler)Harry2009-03-29 20:26:42
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