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allie_96
Pe: 2012-12-02T13:11:38+02:00 In: In:

functie continua

utilizand graficul stabilti daca functia f:R–>R f(x)= x+1, x<1
2x, x>=1 este continua

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  1. xor_NTG
    maestru (V)

    Problema nu e foarte grea. Pur si simplu reprezinti grafic functia si vezi daca exista sau nu intreruperi ale graficului (este sau nu continua).

    O rezolvare de clasa a 11-a:

    Studiem continuitatea in punctul x_1=1

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\[
	\begin{array}{l}
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Emergency stop.

        \[ \left. \begin{array}{l} {\lim }\limits_{ x \to 1 \hfill \atop x > 1 \hfill} f\left( x \right) = 2 \\ {\lim }\limits_{ x \to 1 \hfill \atop x < 1 \hfill} f\left( x \right) = 1 + 1 = 2 \\ \end{array} \right\} \Rightarrow {\lim }\limits_{x \to 1} f\left( x \right) = f\left( 1 \right) \]

    rezulta ca functia este continua.

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