By Edgar W. Bass
ISBN-10: 1418183245
ISBN-13: 9781418183240
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Extra resources for Elements of differential calculus
Example text
A) falsch b) falsch; x 2 · x2 = x 2 c) falsch; 2x · 3x = 6x 2 3 6 d) falsch; (a ) = a e) richtig f) richtig g) richtig h) richtig, denn 22·5 = 45 4. Graph a) b) c) Funktion g f h 5. Graph a) b) c) Funktion h g f 6. 5 · 2t = 2t−1 . 7 Ubungen 7. 3. 1. a) Richtig, denn der Kosinus ist eine gerade Funktion. b) Falsch, denn der Sinus ist eine ungerade Funktion. Daher ist sin(− 2π 3 ) = − sin( 2π ). 3 c) Richtig, denn cos(x) = sin(x + π2 ) 2. a) g(x) = sin(3x) = sin(3x + 2π) = sin(3(x + 23 π)) = g(x + 23 π).
D) cos(2π − x) = cos(x) ..................................... ✻ ....................... ........ ...... . . . ✣ .............. ✡ .... ... ✡ ... .................................. ....... ... .... ✡ ....... .... .. .. ... ... x ... . ✡ ✲ . .. .. .. .. ... ❏ . .... ... ........ . ... ❏ ... .... .... . ❏ . . ....... ❫................. ❏ ........ .......... = cos(x) ..................................... .......... ........
2π .. ... . .. .. ... .... .... ... ........ ....... 15. Sinus- und Kosinusfunktion Eine Kosinusfunktion kann also immer mithilfe einer Sinusfunktion ausgedr¨ uckt werden (und umgekehrt). Wir k¨ onnen daher im Prinzip mit einer der beiden Funktionen auskommen. 33 Sinus und Kosinus a) Dr¨ ucken Sie cos(x − π) durch eine Sinusfunktion aus. b) Dr¨ ucken Sie sin(2x) durch eine Kosinusfunktion aus. 14 um eine halbe Umdrehung gegen den Uhrzeigersinn weiter (addiert also π zum Winkel), so gelangt man zum Punkt −P = (−c, −s).
Elements of differential calculus by Edgar W. Bass
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