Gabriels Horn(endeligt rumfang, uendelig overfladeareal)http://en.wikipedia.org/wiki/Gabriel's_HornFunktionen LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiRRIjFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2JS1JI21pR0YkNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy9GM1EnaXRhbGljRidGO0Y+LyUubGluZXRoaWNrbmVzc0dGMS8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZELyUpYmV2ZWxsZWRHUSZmYWxzZUYnRjI= drejes rundt om x-aksen.Vi ser p\303\245 omr\303\245det: x>1.Definition af funktionenLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==PkkiZkc2ImYqNiNJInhHRiRGJDYkSSlvcGVyYXRvckdGJEkmYXJyb3dHRiRGJCokOSQhIiJGJEYkRiQ=Graf for funktionen (2D)Grafen falder fra v\303\246rdien 1 ned mod 0:LUklcGxvdEc2IjYoLUkiZkdGJDYjSSJ4R0YkL0YpOyIiIiIiJi9JJXZpZXdHRiQ3JDsiIiFGLTtGMiIiIy9JKHNjYWxpbmdHRiRJLGNvbnN0cmFpbmVkR0YkL0kmY29sb3JHRiRJJHJlZEdGJC9JJ2xlZ2VuZEdGJFEpZih4KT0xL3hGJA==Graf for omdrejningslegemet (3D)QyQtSSV3aXRoRzYiNiMmSShTdHVkZW50RzYkSShfc3lzbGliR0YlJSpwcm90ZWN0ZWRHNiNJKkNhbGN1bHVzMUdGJSEiIg==QyQtSTNWb2x1bWVPZlJldm9sdXRpb25HNiI2JyokSSJ4R0YlISIiL0YoOyIiIiIiJi8uSSVheGlzR0YlLkkraG9yaXpvbnRhbEdGJS8uSTFkaXN0YW5jZWZyb21heGlzR0YlIiIhLy5JJ291dHB1dEdGJS5JJXBsb3RHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiVGLA==Rumfang af omdrejningslegemetRumfang beregnes:Metode 1:Med h\303\245ndkraft: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For LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiTkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKCZzcmFycjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GNjYtUSgmaW5maW47RidGOUY7Rj5GQEZCRkRGRkZIRkpGTUY5, vil rumfanget s\303\245ledes n\303\246rme sig 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 2:Maple udf\303\270rer udregningen:PkkoUnVtZmFuZ0c2IiomSSNQaUclKnByb3RlY3RlZEciIiItSSRpbnRHRiQ2JCokLUkiZkdGJDYjSSJ4R0YkIiIjL0YwO0YoSSlpbmZpbml0eUdGJ0YoRumfanget er alts\303\245 endeligt.
Det uendelige horn kan kun rumme \317\200 liter \303\270l !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Overfladeareal af omdrejningslegemetOverfladeareal beregnes:LCQqKEkjUGlHJSpwcm90ZWN0ZWRHIiIiLUkiZkc2IjYjSSJ4R0YpRiYtSSVzcXJ0RzYkRiVJKF9zeXNsaWJHRik2IywmRiZGJiokLUklZGlmZkdGJTYkRidGKyIiI0YmRiZGNg==PkkvT3ZlcmZsYWRlYXJlYWxHNiItSSRpbnRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2JCwkKihJI1BpR0YoIiIiLUkiZkdGJDYjSSJ4R0YkRi4tSSVzcXJ0R0YnNiMsJkYuRi4qJC1JJWRpZmZHRig2JEYvRjIiIiNGLkYuRjsvRjI7Ri5JKWluZmluaXR5R0YoOverfladearealet er alts\303\245 uendeligt!Det kr\303\246ver alts\303\245 uendeligt meget maling at male hornet !