By Isaac Asimov
A millennium into the long run, developments have altered the process human history: the colonization of the Galaxy and the production of the positronic brain. On the attractive Outer international planet of Solaria, a handful of human colonists lead a hermit-like life, their each desire attended to by way of their devoted robotic servants. To this unusual and provocative planet comes Detective Elijah Baley, despatched from the streets of recent York together with his positronic companion, the robotic R. Daneel Olivaw, to resolve a huge homicide that has rocked Solaria to its foundations. The sufferer have been so reclusive that he looked as if it would his affiliates in basic terms via holographic projection. Yet an individual had gotten shut adequate to bludgeon him to dying whereas robots seemed on. Now Baley and Olivaw are confronted with transparent impossibilities: Either the Solarian used to be killed by means of considered one of his robots--unthinkable lower than the legislation of Robotics--or he was once killed through the girl who enjoyed him loads that she by no means got here into his presence!
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Example text
Den Grenzwert s hat, wird dieser Reihe s als Wert zugeschrieben. Wir sagen: Die Reihe konvergiert und hat die Summe s (s ). f ¦ s = a1 a2 a3 .... an .... = k ak (1-34) 1 Sätze über Reihen: f 1. Eine unendliche Reihe ¦ k ak heißt konvergent, wenn ihre Partialsummenfolge 1 < sn > konvergiert. Den Grenzwert s der Partialsummenfolge bezeichnen wir als Summe der Reihe: f ¦ s = a1 a2 a3 .... an .... = k n ak = lim nof 1 sn = ¦ lim nof k ak (1-35) 1 Divergiert dagegen die Folge der Partialsummen der gegebenen Reihe, so heißt diese divergent.
Xn of die Folge < f(xn) > stets gegen denselben Grenzwert G, so heißt G Grenzwert der Funktion für xn ofbzw. xn of. Wir schreiben dafür: lim f ( x) = G bzw. lim xof f ( x) = G (2-10) xof Ist G gleich "+ f"oder "- f ", so sprechen wir auch von einem uneigentlichen Grenzwert. Es gelten hier auch die vorher genannten Grenzwertsätze. b) Eine Gerade g: x = a (Parallele zur y-Achse) heißt Asymptote der Funktion f: y = f(x), wenn gilt: f ( x) = f ; lim xoa lim f ( x) = f (2-11) xoa a heißt Pol der Funktion f.
Auch die Summe, Produkt, Kehrwert und Verkettung (Hintereinanderausführung) von stetigen Funktionen führen wieder auf stetige Funktionen. 1: f ( x) x if 0 d x d 3 f1 ( x) = wenn [ ( 0 d x) ( x d 3) x wenn ( x ! 3 x 1 0) ] oder Funktion x 1 if x ! 5 FRAME lim ( x 1) o 2 x o x1 lim x o x1 f x1 x o3 3 lim 'x o 0 lim 'x o 0 f x1 'x f x1 35 mithilfe der Variablen FRAME definierter Parameter FRAME: 0 bis 15 mit 1 Bild/s x-Wert und y-Wert Differenz rechtsseitiger Grenzwert linksseitiger Grenzwert Funktionswert Der Grenzwert sollte bei Stetigkeit 0 werden!