Gabriels Horn(endeligt rumfang, uendelig overfladeareal)en.wikipedia.org/wiki/Gabriel's_HornFunktionen LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiVRIjFGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYmLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnRjIvRjZRJ2l0YWxpY0YnRj5GMkZBLyUubGluZXRoaWNrbmVzc0dGMS8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZHLyUpYmV2ZWxsZWRHRjRGMkY1 drejes rundt om x-aksen.Man ser p\303\245 omr\303\245det: x>1.Definition af funktionenLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==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Graf for funktionen (2D)Grafen falder fra v\303\246rdien 1 ned mod 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Graf for omdrejningslegemet (3D)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Rumfang af omdrejningslegemetRumfang beregnes: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Rumfanget er alts\303\245 endeligt. Rumfang = LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEnJiM5NjA7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSIuRidGMkY0LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGS0YyRjQ=Gabriels horn kan alts\303\245 rumme en vis m\303\246ngde v\303\246ske.Overfladeareal af omdrejningslegemetOverfladeareal beregnes: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Overfladearealet er alts\303\245 uendeligt!Hvis Gabriels horn skal males, kr\303\246ver det uendelig meget maling!