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sheis_dede
Pe: 2010-10-04T18:32:56+03:00 In: In:

primitive

cum demonstrez ca functia urmatoare e continua :
lim n-> inf cos x+e^nx|x-1| totul supra 1+e^nx

eu tre sa dem ca admite primitive …si zic eu ca ar trb sa arat ca e continua , nu?

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1 raspuns

  1. GreatMath
    veteran (III)

    Am calculat limitele:

        \[ \begin{array}{l} {lim}\limits_{n \to \infty } \frac{{cosx + e^n \cdot x \cdot |x - 1|}}{{1 + e^n \cdot x}} = {lim}\limits_{n \to \infty } \left( {\frac{{cosx}}{{1 + e^n \cdot x}}} \right) + {lim}\limits_{n \to \infty } \left( {\frac{{e^n \cdot x \cdot |x - 1|}}{{1 + e^n \cdot x}}} \right) \\ {lim}\limits_{n \to \infty } \left( {\frac{{cosx}}{{1 + e^n \cdot x}}} \right) = \left( {\cos x} \right) \cdot {lim}\limits_{n \to \infty } \left( {\frac{1}{{1 + e^n \cdot x}}} \right) = 0 \\ {lim}\limits_{n \to \infty } \left( {\frac{{e^n \cdot x \cdot |x - 1|}}{{1 + e^n \cdot x}}} \right) = x \cdot |x - 1| {lim}\limits_{n \to \infty } \left( {\frac{{e^n }}{{1 + e^n \cdot x}}} \right) = \left| {x - 1} \right| \\ \end{array} \]

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