A MathWikiből




2 points Define f(x)=x^3 e^{-x^2} and plot f, f', \ldots f^{(5)}(x) on the interval [ − 2,2]. Use list comprehension for calculating the derivatives and use sum() to add plots into a single picture.


2 points Define a function similar to Collatz:

  • If n is odd, let g(n) = 3n + 1
  • otherwise divide n by the maximum power of 2 which divides n

2^{a_1}\cdot 3^{a_2}\cdot 5^{a_3} \cdot \ldots \mapsto 3^{a_2}\cdot 5^{a_3} \cdot \ldots

For example  53 \rightarrow 160 \rightarrow 5 \rightarrow 16 \rightarrow 1


2 points Find all the Pythagorean triples up to 1000. You need 1000\geq i>j\geq k > 0 where j2 + k2 = i2 and all integers. You cannot list the same triple twice.

Pythagoras 2

2 points Find all the Pythagorean triples up to 100000. Mind that three for up to 100000 would take days, so you need to generate the triples with a formula, see


2018.12.13 Thursday 23:59

Download the solution notebook in a .sws format and attach that.

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