\ubbf8\uc801\ubd84\ud559\uc744 \uacf5\ubd80\ud558\ub2e4 \ubcf4\uba74 \uc218\ub834\ud558\ub294 \uadf9\ud55c\uc744 \uc99d\uba85\ud558\ub294 \uc608\ub97c \uc790\uc8fc \ubcfc \uc218 \uc788\ub2e4. \ubc18\uba74\uc5d0 \ubc1c\uc0b0\ud558\ub294 \uadf9\ud55c\uc744 \uc99d\uba85\ud558\ub294 \uc608\ub294 \uc0c1\ub300\uc801\uc73c\ub85c \uc790\uc8fc \ubcfc \uc218 \uc5c6\ub2e4.<\/p>\n
\uc774 \ud3ec\uc2a4\ud2b8\uc5d0\uc11c\ub294 \ubc1c\uc0b0\ud558\ub294 \uadf9\ud55c\uc744 \uc99d\uba85\ud558\ub294 \uc608\ub97c \uc0b4\ud3b4\ubcf4\uc790. \uc774 \ud3ec\uc2a4\ud2b8\uc5d0\uc11c \ub9d0\ud558\ub294 \u2018\ud568\uc218\u2019\ub294 \ubaa8\ub450 \uacf5\uc5ed\uc774 \uc2e4\uc218 \uc9d1\ud569\uc778 \ud568\uc218\ub97c \ub098\ud0c0\ub0b8\ub2e4.<\/p>\n
\ud568\uc218 \\(f\\)\uac00 \uc810 \\(c\\)\uc758 \uadfc\ucc98\uc5d0\uc11c \uc815\uc758\ub418\uc5c8\ub2e4\uace0 \ud558\uc790. (\uc5c4\ubc00\ud788 \ub9d0\ud558\uba74, \uc810 \\(c\\)\uac00 \\(f\\)\uc758 \uc815\uc758\uc5ed\uc758 \uc9d1\uc801\uc810\uc774\ub77c\uace0 \ud558\uc790.)<\/p>\n
\uc88c\uadf9\ud55c\uacfc \uc6b0\uadf9\ud55c\ub3c4 \ube44\uc2b7\ud558\uac8c \uc815\uc758\ud55c\ub2e4. \uc88c\uadf9\ud55c\uc758 \uacbd\uc6b0 \\(0 < \\lvert x-c \\rvert < \\delta\\)\ub97c \\( c-\\delta < x < c \\)\ub85c \ubc14\uafb8\uba74 \ub418\uace0, \uc6b0\uadf9\ud55c\uc758 \uacbd\uc6b0 \\(0 < \\lvert x-c \\rvert < \\delta\\)\ub97c \\( c < x < c+\\delta \\)\ub85c \ubc14\uafb8\uba74 \ub41c\ub2e4.<\/p>\n
<\/p>\n
\uc608\uc81c 1.<\/span> \ud480\uc774.<\/span> \uc774\uc81c \\( 0 < \\lvert x-0 \\rvert < \\delta\\)\ub77c\uace0 \ud558\uc790. \uadf8\ub7ec\uba74 \\(0 < x^2 < \\delta ^2\\)\uc774\ubbc0\ub85c\n\\[\\frac{1}{x^2} > \\frac{1}{\\delta ^2} = M\\] <\/p>\n \uc608\uc81c 2.<\/span> \ud480\uc774.<\/span> \uc774\uc81c \\( 2 – \\delta < x < 2\\)\ub77c\uace0 \ud558\uc790. \uadf8\ub7ec\uba74 \\(0 > (x-2)^3 > – \\delta ^3\\)\uc774\ubbc0\ub85c \\(x \\rightarrow \\infty\\)\uc778 \uadf9\ud55c\uc774\ub098 \\(x \\rightarrow -\\infty\\)\uc778 \uadf9\ud55c\uc758 \uc815\uc758\ub294, \\(x\\)\uac00 \ud55c \uc810\uc5d0 \ub2e4\uac00\uac00\ub294 \uadf9\ud55c\uc758 \uc815\uc758\ub97c \uc870\uae08 \ubc14\uafb8\uba74 \ub41c\ub2e4.<\/p>\n \ud568\uc218 \\(f\\)\uc758 \uc815\uc758\uc5ed\uc774 \uc704\ub85c \uc720\uacc4\uac00 \uc544\ub2c8\ub77c\uace0 \ud558\uc790. (\uc989, \uc544\ubb34\ub9ac \ud070 \uc591\uc218\ub97c \uc0dd\uac01\ud558\ub354\ub77c\ub3c4 \\(f\\)\uc758 \uc815\uc758\uc5ed\uc5d0 \uadf8 \uc591\uc218\ubcf4\ub2e4 \ub354 \ud070 \uc6d0\uc18c\uac00 \uc874\uc7ac\ud55c\ub2e4\uace0 \ud558\uc790.)<\/p>\n \ud568\uc218 \\(g\\)\uc758 \uc815\uc758\uc5ed\uc774 \uc544\ub798\ub85c \uc720\uacc4\uac00 \uc544\ub2c8\ub77c\uace0 \ud558\uc790. (\uc989, \uc544\ubb34\ub9ac \uc791\uc740 \uc74c\uc218\ub97c \uc0dd\uac01\ud558\ub354\ub77c\ub3c4 \\(g\\)\uc758 \uc815\uc758\uc5ed\uc5d0 \uadf8 \uc74c\uc218\ubcf4\ub2e4 \ub354 \uc791\uc740 \uc6d0\uc18c\uac00 \uc874\uc7ac\ud55c\ub2e4\uace0 \ud558\uc790.)<\/p>\n <\/p>\n \uc608\uc81c 3.<\/span> \ud480\uc774 1.<\/span> \\(X = \\sqrt[3]{M}\\)\uc774\ub77c\uace0 \ud558\uc790. \uadf8\ub7ec\uba74 \\(X\\)\ub294 \uc591\uc218\uc774\ub2e4.<\/p>\n \uc774\uc81c \\(x > X\\)\ub77c\uace0 \ud558\uc790. \uadf8\ub7ec\uba74 \ud480\uc774 2.<\/span> \\(X = \\max \\left\\{ 1 ,\\,\\, M \\right\\}\\)\uc774\ub77c\uace0 \ud558\uc790. \uadf8\ub7ec\uba74 \\(X\\)\ub294 \uc591\uc218\uc774\ub2e4.<\/p>\n \uc774\uc81c \\(x > X\\)\ub77c\uace0 \ud558\uc790. \uadf8\ub7ec\uba74 \\(X \\ge 1\\)\uc774\ubbc0\ub85c \\(x^3 > X^3\\)\uc774\ub2e4.<\/p>\n \ub610\ud55c \\(M \\ge 1\\)\uc77c \ub54c\ub294 \\(X^3 = M^3 \\ge M\\)\uc774\uba70, \\(M < 1\\)\uc77c \ub54c\ub294 \\(X^3 \\ge 1 > M\\)\uc774\ub2e4.<\/p>\n \uadf8\ub7ec\ubbc0\ub85c <\/p>\n \uc608\uc81c 4.<\/span> \ud480\uc774.<\/span> \\(X = \\max \\left\\{ 1,\\,\\, \\ln M \\right\\}\\)\uc774\ub77c\uace0 \ud558\uc790. \uadf8\ub7ec\uba74 \\(X\\)\ub294 \uc591\uc218\uc774\ub2e4.<\/p>\n \uc774\uc81c \\(x < -X\\)\ub77c\uace0 \ud558\uc790. \uadf8\ub7ec\uba74 \\(-x > X > 0\\)\uc774\ubbc0\ub85c \\(x\\rightarrow c\\)\uc77c \ub54c \\(f(x)\\)\uac00 \uc218\ub834\ud558\uc9c0 \uc54a\uace0, \uc591\uc758 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0\ud558\uc9c0 \uc54a\uace0, \uc74c\uc758 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0\ud558\uc9c0\ub3c4 \uc54a\uc73c\uba74, \u201c\\(f(x)\\)\uac00 \uc9c4\ub3d9\ud55c\ub2e4\u201d\ub77c\uace0 \ud45c\ud604\ud55c\ub2e4. \uc5ec\uae30\uc11c \u201c\\(x\\rightarrow c\\)\u201d\ub294 \\(x\\)\uac00 \ud55c \uc810\uc5d0 \ub2e4\uac00\uac00\ub294 \uadf9\ud55c\uc77c \uc218\ub3c4 \uc788\uace0, \uc88c\uadf9\ud55c\uc774\uac70\ub098 \uc6b0\uadf9\ud55c\uc77c \uc218\ub3c4 \uc788\uace0, \\(x\\)\uac00 \ubb34\ud55c\ud788 \ucee4\uc9c0\uac70\ub098 \ubb34\ud55c\ud788 \uc791\uc544\uc9c0\ub294 \uadf9\ud55c\uc77c \uc218\ub3c4 \uc788\ub2e4. \uc9c4\ub3d9\ud558\ub294 \uadf9\ud55c\uc740 \uae30\ud638\ub97c \uc0ac\uc6a9\ud558\uc5ec \ub098\ud0c0\ub0b4\uc9c0 \uc54a\ub294\ub2e4.<\/p>\n \ud568\uc218 \\(f\\)\uac00 \uc9c4\ub3d9\ud568\uc744 \uc99d\uba85\ud558\ub824\uba74 \ub2e4\uc74c \uc138 \uac00\uc9c0\ub97c \ubaa8\ub450 \ubcf4\uc5ec\uc57c \ud55c\ub2e4.<\/p>\n \uc560\ucd08\uc5d0 \u2018\uc9c4\ub3d9\u2019\uc758 \uc815\uc758\uac00 \\(\\epsilon – \\delta\\) \ub17c\ubc95\ucc98\ub7fc \ub531 \ud55c \uc904\ub85c \uc11c\uc220\ub418\ub294 \uac83\uc774 \uc544\ub2c8\ubbc0\ub85c, \ud568\uc218\uac00 \uc9c4\ub3d9\ud55c\ub2e4\ub294 \uc0ac\uc2e4\uc744 \uc99d\uba85\ud560 \ub54c\ub3c4 \\(\\epsilon – \\delta\\) \ub17c\ubc95\uc73c\ub85c \uc99d\uba85\ud560 \ub54c\ucc98\ub7fc \u2018\uc9e7\uace0 \uae54\ub054\u2019\ud55c \uc11c\uc220\ub85c \uc99d\uba85\ud558\uc9c0\ub294 \ubabb\ud55c\ub2e4.<\/p>\n <\/p>\n \uc608\uc81c 5.<\/span> \ud480\uc774.<\/span> \uacb0\ub860\uacfc\ub294 \ubc18\ub300\ub85c \\(x\\rightarrow\\infty\\)\uc77c \ub54c \\(\\sin x\\)\uac00 \uc218\ub834\ud55c\ub2e4\uace0 \uac00\uc815\ud558\uc790. \uadf8\ub9ac\uace0 \uadf9\ud55c\uac12\uc744 \\(L\\)\uc774\ub77c\uace0 \ud558\uc790. \\(\\epsilon = \\frac{1}{2}\\)\uc774\ub77c\uace0 \ub450\uba74 \\(\\epsilon > 0\\)\uc774\ubbc0\ub85c, \uc218\ub834\ud558\ub294 \uadf9\ud55c\uc758 \uc815\uc758\ub97c \ub9cc\uc871\uc2dc\ud0a4\ub294 \uc591\uc218 \\(X\\)\uac00 \uc874\uc7ac\ud55c\ub2e4. \uadf8\ub7ec\uba74 \\(x > X\\)\uc778 \ubaa8\ub4e0 \\(x\\)\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c\uc73c\ub85c \\(x\\rightarrow \\infty\\)\uc77c \ub54c \\(\\sin x\\)\uac00 \uc591\uc758 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0\ud558\uc9c0 \uc54a\uc74c\uc744 \ubcf4\uc774\uc790.<\/p>\n \uacb0\ub860\uacfc\ub294 \ubc18\ub300\ub85c \\(x\\rightarrow \\infty\\)\uc77c \ub54c \\(\\sin x\\)\uac00 \uc591\uc758 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0\ud55c\ub2e4\uace0 \uac00\uc815\ud558\uc790. \uadf8\ub9ac\uace0 \\(M = 1\\)\uc774\ub77c\uace0 \ud558\uc790. \uadf8\ub7ec\uba74 \uc591\uc758 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0\ud558\ub294 \uadf9\ud55c\uc758 \uc815\uc758\ub97c \ub9cc\uc871\uc2dc\ud0a4\ub294 \uc591\uc218 \\(X\\)\uac00 \uc874\uc7ac\ud558\uba70, \\(x > X\\)\uc778 \ubaa8\ub4e0 \\(x\\)\uc5d0 \ub300\ud558\uc5ec \\(\\sin x > M\\)\uc774 \uc131\ub9bd\ud55c\ub2e4. \uadf8\ub7f0\ub370 \\(\\sin x\\)\uc758 \uac12\uc740 \\(1\\)\uc744 \ucd08\uacfc\ud560 \uc218 \uc5c6\uc73c\ubbc0\ub85c, \uc774\uac83\uc740 \ubaa8\uc21c\uc774\ub2e4. \uadf8\ub7ec\ubbc0\ub85c \\(x\\rightarrow \\infty\\)\uc77c \ub54c \\(\\sin x\\)\uac00 \uc591\uc758 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0\ud558\uc9c0 \uc54a\ub294\ub2e4.<\/p>\n \uac19\uc740 \ubc29\ubc95\uc73c\ub85c \\(x\\rightarrow \\infty\\)\uc77c \ub54c \\(\\sin x\\)\uac00 \uc74c\uc758 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0\ud558\uc9c0 \uc54a\uc74c\uc744 \ubcf4\uc77c \uc218 \uc788\ub2e4.<\/p>\n \uc774\ub85c\uc368 \\(x\\rightarrow \\infty\\)\uc77c \ub54c \\(\\sin x\\)\uac00 \uc218\ub834\ud558\uc9c0 \uc54a\uace0, \uc591\uc758 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0\ud558\uc9c0 \uc54a\uace0, \uc74c\uc758 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0\ud558\uc9c0\ub3c4 \uc54a\uc73c\ubbc0\ub85c, \\(x\\rightarrow \\infty\\)\uc77c \ub54c \\(\\sin x\\)\ub294 \uc9c4\ub3d9\ud55c\ub2e4.\n<\/p>\n<\/div>\n <\/p>\n \uc608\uc81c 6.<\/span> \ud480\uc774.<\/span> \uacb0\ub860\uacfc\ub294 \ubc18\ub300\ub85c \\(x\\rightarrow n\\)\uc77c \ub54c \\(\\lfloor x \\rfloor\\)\uac00 \uc218\ub834\ud55c\ub2e4\uace0 \uac00\uc815\ud558\uc790. \uadf8\ub9ac\uace0 \uadf9\ud55c\uac12\uc744 \\(L\\)\uc774\ub77c\uace0 \ud558\uc790. \\(\\epsilon = \\frac{1}{2}\\)\uc774\ub77c\uace0 \ub450\uba74 \\(\\epsilon > 0\\)\uc774\ubbc0\ub85c, \uc218\ub834\ud558\ub294 \uadf9\ud55c\uc758 \uc815\uc758\ub97c \ub9cc\uc871\uc2dc\ud0a4\ub294 \uc591\uc218 \\(\\delta\\)\uac00 \uc874\uc7ac\ud55c\ub2e4. \uadf8\ub7ec\uba74 \\( 0 < \\lvert x-n \\rvert < \\delta\\)\uc778 \ubaa8\ub4e0 \\(x\\)\uc5d0 \ub300\ud558\uc5ec\n\\[\\lvert \\lfloor x \\rfloor - L \\rvert < \\epsilon\\]\n\uc989\n\\[ L - \\frac{1}{2} < \\lfloor x \\rfloor < L + \\frac{1}{2}\\]\n\uc774 \uc131\ub9bd\ud55c\ub2e4. \ub9cc\uc57d \\(x\\)\uac00 \\( 0 < \\lvert x-n \\rvert < \\delta\\)\uc774\uba74\uc11c \\(n-1 < x < n\\)\uc778 \ubc94\uc704\uc5d0 \uc788\uc73c\uba74 \\[\\lfloor x \\rfloor = n-1\\]\n\uc774\ubbc0\ub85c\n\\[L - \\frac{1}{2} < n-1\\]\n\uc989\n\\[L < n - \\frac{1}{2}\\tag{a}\\]\n\uc774 \uc131\ub9bd\ud55c\ub2e4. \ub9cc\uc57d \\(x\\)\uac00 \\( 0 < \\lvert x-n \\rvert < \\delta\\)\uc774\uba74\uc11c \\(n < x < n+1\\)\uc778 \ubc94\uc704\uc5d0 \uc788\uc73c\uba74 \\[\\lfloor x \\rfloor = n\\]\n\uc774\ubbc0\ub85c\n\\[n < L + \\frac{1}{2}\\]\n\uc989\n\\[n - \\frac{1}{2} < L\\tag{b}\\]\n\uc774 \uc131\ub9bd\ud55c\ub2e4. \ub450 \ubd80\ub4f1\uc2dd (a), (b)\ub97c \uacb0\ud569\ud558\uba74\n\\[L < n - \\frac{1}{2} < L\\]\n\uc774\ubbc0\ub85c \ubaa8\uc21c\uc774\ub2e4. \uadf8\ub7ec\ubbc0\ub85c \\(x \\rightarrow n\\)\uc77c \ub54c \\(\\lfloor x \\rfloor\\)\ub294 \uc218\ub834\ud558\uc9c0 \uc54a\ub294\ub2e4.\n \n\n \ub2e4\uc74c\uc73c\ub85c \\(x\\rightarrow n\\)\uc77c \ub54c \\(\\lfloor x \\rfloor\\)\uac00 \uc591\uc758 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0\ud558\uc9c0 \uc54a\uc74c\uc744 \uc99d\uba85\ud558\uc790.<\/p>\n \\(M = n+1\\)\uc774\ub77c\uace0 \ud558\uc790. \uadf8\ub7ec\uba74 \\(M > 0\\)\uc774\ubbc0\ub85c, \uc591\uc758 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0\ud558\ub294 \uadf9\ud55c\uc758 \uc815\uc758\ub97c \ub9cc\uc871\uc2dc\ud0a4\ub294 \uc591\uc218 \\(\\delta\\)\uac00 \uc874\uc7ac\ud558\uc5ec, \\(0 < \\lvert x-n \\rvert < \\delta\\)\uc77c \ub54c\ub9c8\ub2e4\n\\[\\lfloor x \\rfloor > M\\tag{c}\\] \ube44\uc2b7\ud55c \ubc29\ubc95\uc73c\ub85c \\(x\\rightarrow n\\)\uc77c \ub54c \\(\\lfloor x \\rfloor\\)\uac00 \uc74c\uc758 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0\ud558\uc9c0 \uc54a\uc74c\uc744 \ubcf4\uc77c \uc218 \uc788\ub2e4.<\/p>\n<\/div>\n \ud568\uc218\uac00 \uc9c4\ub3d9\ud55c\ub2e4\ub294 \uc0ac\uc2e4\uc744 \uc99d\uba85\ud560 \ub54c \ub2e4\uc74c\uacfc \uac19\uc740 \uc815\ub9ac\ub97c \uc0ac\uc6a9\ud558\uba74 \uc720\uc6a9\ud558\ub2e4.<\/p>\n \ud568\uc218\uc758 \uadf9\ud55c\uacfc \uad00\ub828\ub41c \uba87 \uac00\uc9c0 \uc815\ub9ac<\/span><\/p>\n \uc704 \uc815\ub9ac \uc911 \uccab \ubc88\uc9f8 \uc815\ub9ac\uc640 \ub450 \ubc88\uc9f8 \uc815\ub9ac\uc5d0\uc11c \\(c\\)\ub294 \ubaa8\ub450 \uace0\uc815\ub41c \uc810(\uc2e4\uc218)\uc774\ub2e4. \uc138 \ubc88\uc7ac \uc815\ub9ac\uc640 \ub124 \ubc88\uc9f8 \uc815\ub9ac\uc758 \uacbd\uc6b0 \\(c\\)\ub97c \uc591\uc758 \ubb34\ud55c\ub300\ub098 \uc74c\uc758 \ubb34\ud55c\ub300\ub85c \ubc14\uafc0 \uc218 \uc788\ub2e4. \uc774\ub54c \u201c\\(\\left\\{ x_n \\right\\}\\)\uc774 \\(c\\)\uc5d0 \uc218\ub834\ud55c\ub2e4\u201d\ub77c\ub294 \ud45c\ud604\uc740 \u201c\\(\\left\\{ x_n \\right\\}\\)\uc774 \\(c\\)\ub85c \ubc1c\uc0b0\ud55c\ub2e4\u201d\ub85c \ubc14\uafb8\uba74 \ub41c\ub2e4.<\/p>\n \uc608\uc81c 6\uc758 \ub2e4\ub978 \ud480\uc774.<\/span> \ud55c\ud3b8 \\(x \\rightarrow n\\)\uc77c \ub54c \\(\\lfloor x \\rfloor\\)\uc758 \uc88c\uadf9\ud55c\uacfc \uc6b0\uadf9\ud55c\uc774 \uac01\uac01 \uc218\ub834\ud558\ubbc0\ub85c, \\(x \\rightarrow n\\)\uc77c \ub54c \\(\\lfloor x \\rfloor\\)\ub294 \uc591\uc758 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0\ud558\uc9c0 \uc54a\uace0, \uc74c\uc758 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0\ud558\uc9c0\ub3c4 \uc54a\ub294\ub2e4.\n<\/p>\n<\/div>\n <\/p>\n \uc608\uc81c 7.<\/span> \ud480\uc774.<\/span> \ub2e4\uc74c\uc73c\ub85c \\(x\\rightarrow 3\\)\uc77c \ub54c \\(f(x)\\)\uac00 \uc591\uc758 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0\ud558\uc9c0 \uc54a\uc74c\uc744 \ubcf4\uc774\uc790. \\(M = 1\\)\uc774\ub77c\uace0 \ud558\uc790. \uadf8\ub7ec\uba74 \uc591\uc218 \\(\\delta\\)\ub97c \uc5b4\ub290 \uac12\uc73c\ub85c \uc124\uc815\ud558\ub4e0, \\( 0 < \\lvert x-3 \\rvert < \\delta\\)\ub97c \ub9cc\uc871\uc2dc\ud0a4\ub294 \\(x\\)\uc5d0 \ub300\ud558\uc5ec \\(f(x) \\le M\\)\uc774\ub2e4. \uc989 \ud568\uc22b\uac12 \\(f(x)\\)\uac00 \\(M\\)\uc744 \ucd08\uacfc\ud560 \uc218 \uc5c6\ub2e4. \uadf8\ub7ec\ubbc0\ub85c \\(x\\rightarrow 3\\)\uc77c \ub54c \\(f(x)\\)\ub294 \uc591\uc758 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0\ud558\uc9c0 \uc54a\ub294\ub2e4.<\/p>\n \ube44\uc2b7\ud55c \ubc29\ubc95\uc73c\ub85c \\(x\\rightarrow 3\\)\uc77c \ub54c \\(f(x)\\)\uac00 \uc74c\uc758 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0\ud558\uc9c0 \uc54a\uc74c\uc744 \ubcf4\uc77c \uc218 \uc788\ub2e4.\n<\/p>\n<\/div>\n <\/p>\n \uc608\uc81c 8.<\/span> \ud480\uc774.<\/span> \ub2e4\uc74c\uc73c\ub85c <\/p>\n","protected":false},"excerpt":{"rendered":" \ubbf8\uc801\ubd84\ud559\uc744 \uacf5\ubd80\ud558\ub2e4 \ubcf4\uba74 \uc218\ub834\ud558\ub294 \uadf9\ud55c\uc744 \uc99d\uba85\ud558\ub294 \uc608\ub97c \uc790\uc8fc \ubcfc \uc218 \uc788\ub2e4. \ubc18\uba74\uc5d0 \ubc1c\uc0b0\ud558\ub294 \uadf9\ud55c\uc744 \uc99d\uba85\ud558\ub294 \uc608\ub294 \uc0c1\ub300\uc801\uc73c\ub85c \uc790\uc8fc \ubcfc \uc218 \uc5c6\ub2e4. \uc774 \ud3ec\uc2a4\ud2b8\uc5d0\uc11c\ub294 \ubc1c\uc0b0\ud558\ub294 \uadf9\ud55c\uc744 \uc99d\uba85\ud558\ub294 \uc608\ub97c \uc0b4\ud3b4\ubcf4\uc790. \uc774 \ud3ec\uc2a4\ud2b8\uc5d0\uc11c \ub9d0\ud558\ub294 \u2018\ud568\uc218\u2019\ub294 \ubaa8\ub450 \uacf5\uc5ed\uc774 \uc2e4\uc218 \uc9d1\ud569\uc778 \ud568\uc218\ub97c \ub098\ud0c0\ub0b8\ub2e4. \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0\ud558\ub294 \uadf9\ud55c \ud568\uc218 \\(f\\)\uac00 \uc810 \\(c\\)\uc758 \uadfc\ucc98\uc5d0\uc11c \uc815\uc758\ub418\uc5c8\ub2e4\uace0 \ud558\uc790. (\uc5c4\ubc00\ud788 \ub9d0\ud558\uba74, \uc810 \\(c\\)\uac00 \\(f\\)\uc758 \uc815\uc758\uc5ed\uc758 \uc9d1\uc801\uc810\uc774\ub77c\uace0 \ud558\uc790.) \ub9cc\uc57d \uc784\uc758\uc758 \uc591\uc218 \\(M\\)\uc5d0 \ub300\ud558\uc5ec, \uc591\uc218 \\(\\delta\\)\uac00 \uc874\uc7ac\ud558\uc5ec,…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"categories":[47],"tags":[126,138,139],"class_list":["post-9083","post","type-post","status-publish","format-standard","hentry","category-calculus-ap","tag-126","tag-138","tag-139"],"_links":{"self":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/posts\/9083","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/comments?post=9083"}],"version-history":[{"count":67,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/posts\/9083\/revisions"}],"predecessor-version":[{"id":9156,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/posts\/9083\/revisions\/9156"}],"wp:attachment":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/media?parent=9083"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/categories?post=9083"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/tags?post=9083"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\ub2e4\uc74c \uadf9\ud55c\uc744 \uc99d\uba85\ud558\uc2dc\uc624.
\n\\[\\lim_{x\\rightarrow 0} \\frac{1}{x^2} = \\infty \\]\n<\/p>\n<\/div>\n
\n\uc591\uc218 \\(M\\)\uc774 \uc784\uc758\ub85c \uc8fc\uc5b4\uc84c\ub2e4\uace0 \ud558\uc790.
\n\\[\\delta = \\frac{1}{\\sqrt{M}}\\]
\n\uc774\ub77c\uace0 \ud558\uc790. \uadf8\ub7ec\uba74 \\(\\delta\\)\ub294 \uc591\uc218\uc774\ub2e4.<\/p>\n
\n\uc774\ub2e4. \uadf8\ub7ec\ubbc0\ub85c \\(x \\rightarrow 2-\\)\uc77c \ub54c \\(\\frac{1}{(x-2)^3}\\)\uc774 \uc74c\uc758 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0\ud55c\ub2e4.\n<\/p>\n<\/div>\n
\n\ub2e4\uc74c \uadf9\ud55c\uc744 \uc99d\uba85\ud558\uc2dc\uc624.
\n\\[\\lim_{x\\rightarrow 2-} \\frac{1}{(x-2)^3} = – \\infty \\]\n<\/p>\n<\/div>\n
\n\uc591\uc218 \\(M\\)\uc774 \uc784\uc758\ub85c \uc8fc\uc5b4\uc84c\ub2e4\uace0 \ud558\uc790.
\n\\[\\delta = \\frac{1}{\\sqrt[3]{M}}\\]
\n\uc774\ub77c\uace0 \ud558\uc790(\ubd84\ubaa8\uac00 \\(M\\)\uc758 \uc138\uc81c\uacf1\uadfc\uc774\ub2e4). \uadf8\ub7ec\uba74 \\(\\delta\\)\ub294 \uc591\uc218\uc774\ub2e4.<\/p>\n
\n\\[\\frac{1}{(x-2)^3} < - \\frac{1}{\\delta ^3} = - M\\]\n\uc774\ub2e4. \uadf8\ub7ec\ubbc0\ub85c \\(x \\rightarrow 0\\)\uc77c \ub54c \\(\\frac{1}{x^2} \\rightarrow \\infty\\)\uc774\ub2e4.\n<\/p>\n<\/div>\n\n
\n\\[\\lim_{x\\rightarrow \\infty} f(x)= \\infty\\]
\n\uc640 \uac19\uc774 \ub098\ud0c0\ub0b8\ub2e4.<\/li>\n\n
\n\\[\\lim_{x\\rightarrow -\\infty} g(x)= \\infty\\]
\n\uc640 \uac19\uc774 \ub098\ud0c0\ub0b8\ub2e4.<\/li>\n
\n\ub2e4\uc74c \uadf9\ud55c\uc744 \uc99d\uba85\ud558\uc2dc\uc624.
\n\\[\\lim_{x\\rightarrow \\infty} x^3 = \\infty \\]\n<\/p>\n<\/div>\n
\n\uc591\uc218 \\(M\\)\uc774 \uc784\uc758\ub85c \uc8fc\uc5b4\uc84c\ub2e4\uace0 \ud558\uc790.<\/p>\n
\n\\[x^3 > X^3 = M\\]
\n\uc774\ub2e4. \uadf8\ub7ec\ubbc0\ub85c \\(x\\rightarrow\\infty\\)\uc77c \ub54c \\(x^3 \\rightarrow \\infty\\)\uc774\ub2e4.\n<\/p>\n<\/div>\n
\n\uc591\uc218 \\(M\\)\uc774 \uc784\uc758\ub85c \uc8fc\uc5b4\uc84c\ub2e4\uace0 \ud558\uc790.<\/p>\n
\n\\[x^3 > X^3 \\ge M\\]
\n\uc774\ub2e4. \ub530\ub77c\uc11c \\(x\\rightarrow\\infty\\)\uc77c \ub54c \\(x^3\\)\uc740 \uc591\uc758 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0\ud55c\ub2e4.\n<\/p>\n<\/div>\n
\n\ub2e4\uc74c \uadf9\ud55c\uc744 \uc99d\uba85\ud558\uc2dc\uc624.
\n\\[\\lim_{x\\rightarrow – \\infty} e^{-x} = \\infty \\]\n<\/p>\n<\/div>\n
\n\uc591\uc218 \\(M\\)\uc774 \uc784\uc758\ub85c \uc8fc\uc5b4\uc84c\ub2e4\uace0 \ud558\uc790.<\/p>\n
\n\\[e^{-x} > e^X \\ge e^{\\ln M} = M\\]
\n\uc774\ub2e4. \uadf8\ub7ec\ubbc0\ub85c \\(x \\rightarrow -\\infty\\)\uc77c \ub54c \\(e^{-x} \\rightarrow \\infty\\)\uc774\ub2e4.\n<\/p>\n<\/div>\n\uc9c4\ub3d9\ud558\ub294 \uadf9\ud55c<\/h3>\n
\n
\n\\(x \\rightarrow \\infty\\)\uc77c \ub54c \\(\\sin x\\)\uac00 \uc9c4\ub3d9\ud568\uc744 \uc99d\uba85\ud558\uc2dc\uc624.\n<\/p>\n<\/div>\n
\n\uc6b0\uc120 \\(\\sin x\\)\uac00 \uc218\ub834\ud558\uc9c0 \uc54a\ub294\ub2e4\ub294 \uc0ac\uc2e4\uc744 \uc99d\uba85\ud558\uc790.<\/p>\n
\n\\[\\lvert \\sin x – L \\rvert < \\epsilon = \\frac{1}{2}\\]\n\uc989\n\\[- \\frac{1}{2} < \\sin x - L < \\frac{1}{2}\\]\n\uc774 \uc131\ub9bd\ud574\uc57c \ud55c\ub2e4. \uc774 \ubd80\ub4f1\uc2dd\uc744 \ub450 \uac1c\uc758 \ubd80\ub4f1\uc2dd\uc73c\ub85c \ub098\ud0c0\ub0b4\uba74\n\\[ L < \\sin x + \\frac{1}{2} , \\quad \\sin x - \\frac{1}{2} < L\\]\n\uc774\ub2e4. \\(X\\)\uac00 \uc5b4\ub5a4 \uac12\uc774\ub4e0 \uc0c1\uad00 \uc5c6\uc774 \\(x > X\\)\uc778 \ubc94\uc704\uc5d0\uc11c \\(\\sin x\\)\uac00 \\(-1\\)\ubd80\ud130 \\(1\\)\uae4c\uc9c0 \ubaa8\ub4e0 \uac12\uc744 \uac00\uc9c8 \uc218 \uc788\uc73c\ubbc0\ub85c, \uccab \ubc88\uc9f8 \ubd80\ub4f1\uc2dd\uc73c\ub85c\ubd80\ud130
\n\\[L < -1 + \\frac{1}{2} = - \\frac{1}{2}\\]\n\uc744 \uc5bb\uc73c\uba70, \ub450 \ubc88\uc9f8 \ubd80\ub4f1\uc2dd\uc73c\ub85c\ubd80\ud130\n\\[L > 1 – \\frac{1}{2} = \\frac{1}{2}\\]
\n\uc744 \uc5bb\ub294\ub2e4. \uc989
\n\\[\\frac{1}{2} < L < - \\frac{1}{2}\\]\n\uc774\ubbc0\ub85c \ubaa8\uc21c\uc774\ub2e4. \ub530\ub77c\uc11c \\(x\\rightarrow \\infty\\)\uc77c \ub54c \\(\\sin x\\)\ub294 \uc218\ub834\ud558\uc9c0 \uc54a\ub294\ub2e4.<\/p>\n
\n\\(n\\)\uc774 \uc815\uc218\uc774\uace0 \\(f(x) = \\lfloor x \\rfloor\\)\uac00 \ucd5c\ub300\uc815\uc218 \ud568\uc218(\uac00\uc6b0\uc2a4 \ud568\uc218)\ub77c\uace0 \ud558\uc790. \\(x \\rightarrow n\\)\uc77c \ub54c \\(f(x)\\)\uac00 \uc9c4\ub3d9\ud568\uc744 \uc99d\uba85\ud558\uc2dc\uc624.\n<\/p>\n<\/div>\n
\n\uc6b0\uc120 \\(\\lfloor x \\rfloor\\)\uac00 \uc218\ub834\ud558\uc9c0 \uc54a\ub294\ub2e4\ub294 \uc0ac\uc2e4\uc744 \uc99d\uba85\ud558\uc790.<\/p>\n
\n\uc774 \uc131\ub9bd\ud55c\ub2e4. \uadf8\ub7f0\ub370 \\(x\\)\uc640 \\(n\\)\uc758 \uac70\ub9ac\uac00 \\(1\\) \ubbf8\ub9cc\uc774\uba74 \\(\\lfloor x \\rfloor\\)\uc758 \uac12\uc740 \\(M = n+1\\)\ubcf4\ub2e4 \ucee4\uc9c8 \uc218 \uc5c6\ub2e4. \uadf8\ub7ec\ubbc0\ub85c \\(0 < \\lvert x-n \\rvert < \\delta\\)\uc77c \ub54c\ub9c8\ub2e4 (c)\uac00 \uc131\ub9bd\ud558\ub3c4\ub85d \ud558\ub294 \uc591\uc218 \\(\\delta\\)\ub294 \uc874\uc7ac\ud558\uc9c0 \uc54a\ub294\ub2e4. \uc989 \\(x\\rightarrow n\\)\uc77c \ub54c \\(\\lfloor x \\rfloor\\)\uac00 \uc591\uc758 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0\ud558\uc9c0 \uc54a\ub294\ub2e4.<\/p>\n\n
\n\\(x \\rightarrow n-\\)\uc77c \ub54c \\(\\lfloor x \\rfloor \\rightarrow n-1\\)\uc774\uace0, \\(x \\rightarrow n+\\)\uc77c \ub54c \\(\\lfloor x \\rfloor \\rightarrow n\\)\uc774\uace0, \\(n\\)\uc5d0\uc11c \\(\\lfloor x \\rfloor\\)\uc758 \uc88c\uadf9\ud55c\uacfc \uc6b0\uadf9\ud55c\uc774 \ub2e4\ub974\ub2e4. \uadf8\ub7ec\ubbc0\ub85c \\(x\\rightarrow n\\)\uc77c \ub54c \\(\\lfloor x \\rfloor\\)\ub294 \uc218\ub834\ud558\uc9c0 \uc54a\ub294\ub2e4.<\/p>\n
\n\ud568\uc218 \\(f:\\mathbb{R} \\rightarrow \\mathbb{R}\\)\uac00 \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ub418\uc5b4 \uc788\ub2e4\uace0 \ud558\uc790.
\n\\[f(x)=
\n\\begin{cases}
\n1 \\quad & \\mathrm{if} \\,\\, x \\in \\mathbb{Q} ,\\\\[6pt]
\n0 \\quad & \\mathrm{if} \\,\\, x \\notin \\mathbb{Q} .
\n\\end{cases}
\n\\]
\n\\(x\\rightarrow 3\\)\uc77c \ub54c \\(f(x)\\)\uac00 \uc9c4\ub3d9\ud568\uc744 \uc99d\uba85\ud558\uc2dc\uc624.\n<\/p>\n<\/div>\n
\n\\(x\\rightarrow 3\\)\uc77c \ub54c \\(f(x)\\)\uac00 \uc218\ub834\ud55c\ub2e4\uace0 \uac00\uc815\ud558\uace0, \uadf9\ud55c\uac12\uc744 \\(L\\)\uc774\ub77c\uace0 \ud558\uc790. \uadf8\ub9ac\uace0
\n\\[q_n = 3+ \\frac{1}{n} , \\quad r_n = 3+ \\frac{\\pi}{n}\\]
\n\ub77c\uace0 \ud558\uc790. \uadf8\ub7ec\uba74 \\(\\left\\{ q_n \\right\\}\\)\uc740 \\(3\\)\uc5d0 \uc218\ub834\ud558\ub294 \uc720\ub9ac\uc218\uc5f4\uc774\uace0, \\(\\left\\{ r_n \\right\\}\\)\uc740 \\(3\\)\uc5d0 \uc218\ub834\ud558\ub294 \ubb34\ub9ac\uc218\uc5f4\uc774\ub2e4. \uadf8\ub7ec\ubbc0\ub85c \ub450 \uc218\uc5f4 \\(\\left\\{ f(q_n ) \\right\\}\\)\uacfc \\(\\left\\{ f(r_n ) \\right\\}\\)\uc740 \ubaa8\ub450 \uac19\uc740 \uac12 \\(L\\)\uc5d0 \uc218\ub834\ud574\uc57c \ud55c\ub2e4. \uadf8\ub7f0\ub370 \uc784\uc758\uc758 \uc790\uc5f0\uc218 \\(n\\)\uc5d0 \ub300\ud558\uc5ec
\n\\[f(q_n ) = 1 ,\\quad f(r_n ) =0\\]
\n\uc774\ubbc0\ub85c, \\(\\left\\{ f(q_n ) \\right\\}\\)\uacfc \\(\\left\\{ f(r_n ) \\right\\}\\)\uc740 \uac01\uac01 \\(1\\)\uacfc \\(0\\)\uc5d0 \uc218\ub834\ud55c\ub2e4. \uadf8\ub7ec\ubbc0\ub85c \\(x\\rightarrow 3\\)\uc77c \ub54c \\(f(x)\\)\ub294 \uc218\ub834\ud558\uc9c0 \uc54a\ub294\ub2e4.<\/p>\n
\n\ud568\uc218 \\(f:\\mathbb{R} \\rightarrow \\mathbb{R}\\)\uac00 \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ub418\uc5b4 \uc788\ub2e4\uace0 \ud558\uc790.
\n\\[f(x) = x + x \\sin x.\\]
\n\\(x\\rightarrow \\infty\\)\uc77c \ub54c \\(f(x)\\)\uac00 \uc9c4\ub3d9\ud568\uc744 \uc99d\uba85\ud558\uc2dc\uc624.\n<\/p>\n<\/div>\n
\n\\[p_n = 2n\\pi + \\frac{1}{2} \\pi\\]
\n\ub77c\uace0 \ud558\uba74 \\(\\left\\{ p_n \\right\\}\\)\uc740 \uc591\uc758 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0\ud558\ub294 \uc218\uc5f4\uc774\ub2e4. \uadf8\ub7f0\ub370
\n\\[f( p_n ) = \\left( 2n\\pi + \\frac{1}{2} \\pi \\right) + \\left( 2n\\pi + \\frac{1}{2} \\pi \\right)\\]
\n\uc774\ubbc0\ub85c, \\(\\left\\{ f(p_n )\\right\\}\\)\uc740 \uc591\uc758 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0\ud55c\ub2e4. \uadf8\ub7ec\ubbc0\ub85c \\(x\\rightarrow\\infty\\)\uc77c \ub54c \\(f(x)\\)\ub294 \uc218\ub834\ud558\uc9c0 \uc54a\ub294\ub2e4.<\/p>\n
\n\\[q_n = 2n\\pi + \\frac{3}{2} \\pi\\]
\n\ub77c\uace0 \ud558\uba74 \\(\\left\\{ q_n \\right\\}\\)\uc740 \uc591\uc758 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0\ud558\ub294 \uc218\uc5f4\uc774\ub2e4. \uadf8\ub7f0\ub370
\n\\[f( q_n ) = \\left( 2n\\pi + \\frac{3}{2} \\pi \\right) – \\left( 2n\\pi + \\frac{3}{2} \\pi \\right) = 0\\]
\n\uc774\ubbc0\ub85c, \\(\\left\\{ f(q_n )\\right\\}\\)\uc740 \\(0\\)\uc5d0 \uc218\ub834\ud55c\ub2e4. \uadf8\ub7ec\ubbc0\ub85c \\(x\\rightarrow\\infty\\)\uc77c \ub54c \\(f(x)\\)\ub294 \uc591\uc758 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0\ud558\uc9c0 \uc54a\uace0, \uc74c\uc758 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0\ud558\uc9c0\ub3c4 \uc54a\ub294\ub2e4.\n<\/p>\n<\/div>\n\uc5f0\uc2b5\ubb38\uc81c<\/h3>\n
\n
\ud0d0\uad6c\ubb38\uc81c<\/h3>\n
\n