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auranonima
Pe: 2013-03-06T21:05:28+02:00 In: In:

problema de sinteza la analiza

Fie functia 

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Emergency stop.

si sirul

    \[ \begin{array}{l} (I_n )_{n \ge 1} , \ I_n = \int\limits_0^1 {f^n (x)dx} \\ \end{array} \]

.
a) Sa se arate ca

    \[ 0 \le x - x^2 \le \frac{1}{4}, \forall x \in \left[ {0,1} \right] \]

b)Sa se arate ca

    \[ 0 \le I_n \le \frac{1}{{4^n }},\forall n \in N* \]

c)sa se calculeze

    \[ {\lim }\limits_{x \to \infty } I_n \]

d)sa se arate ca

    \[ I_n = \frac{1}{4} \cdot \frac{{2n}}{{2n + 1}} \cdot I_{n - 1,} \forall n \in N*,n \ge 2 \]

e)sa se arate ca

    \[ I_n \in Q \]

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2 raspunsuri

  1. DD
    profesor

    Attached files

  2. auranonima

    Multumesc!

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