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한명수

Posted at 2012-01-16 09:56:18

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이현녀 선생님의 답글입니다.   예제. <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=105 align=absMiddle height=18><PARAM NAME="_cx" VALUE="2778"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="4063280"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/23.4`4.3/12,[1]{left vbar{y-1}right vbar`equal`x-a}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT>의 그래프와 <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=12 align=absMiddle height=18><PARAM NAME="_cx" VALUE="317"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/2.8`4.3/12,[1]{y}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT>축으로 둘러싸인 부분의 넓이가 4일 때, <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=12 align=absMiddle height=18><PARAM NAME="_cx" VALUE="317"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/2.8`4.3/12,[1]{a}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT>의 값을 구하여라.   이런 문제는 수학적 사고를 해야하는 문제로 아주 좋네요. 먼저 절대값은 절대값 기호 안의 식이 양수일 때와 음수일 때로 나누어 생각해야합니다. i) <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=70 align=absMiddle height=18><PARAM NAME="_cx" VALUE="1852"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/15.8`4.3/12,[1]{y-1`gt`0}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT> <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=97 align=absMiddle height=18><PARAM NAME="_cx" VALUE="2566"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/21.4`4.3/12,[1]{y-1`equal`x-a}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT>, <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=97 align=absMiddle height=18><PARAM NAME="_cx" VALUE="2566"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/21.4`4.3/12,[1]{y`equal`x-a`plus`1}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT> ii) <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=70 align=absMiddle height=18><PARAM NAME="_cx" VALUE="1852"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/15.8`4.3/12,[1]{y-1`lt`0}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT> <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=109 align=absMiddle height=18><PARAM NAME="_cx" VALUE="2883"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="4063280"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/24.1`4.3/12,[1]{-y`plus`1`equal`x-a}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT>, <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=109 align=absMiddle height=18><PARAM NAME="_cx" VALUE="2883"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="4063280"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/24.1`4.3/12,[1]{y`equal`-x`plus`a`plus`1}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT> i) 식은 기울기가 1 이고, ii) 식의 기울기는 -1 이다. 즉 i) 식은 증가함수이고, ii) 식은 감소함수이다. 그런데 이 두 식과 <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=12 align=absMiddle height=18><PARAM NAME="_cx" VALUE="317"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/2.8`4.3/12,[1]{y}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT>축으로 둘러싸인 부분의 넓이가 4 이므로 i), ii) 식은 만나야 하고 만나는 점은 <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=41 align=absMiddle height=18><PARAM NAME="_cx" VALUE="1084"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/9.2`4.3/12,[1]{y`equal`1}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT>인 점이다. 또한 만나는 점 <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=41 align=absMiddle height=18><PARAM NAME="_cx" VALUE="1084"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/9.2`4.3/12,[1]{y`equal`1}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT> 의   <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=12 align=absMiddle height=18><PARAM NAME="_cx" VALUE="317"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/2.8`4.3/12,[1]{x}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT>의 좌표는 0 보다 작아야 둘러싸인 부분이 만들어진다. 따라서 <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=41 align=absMiddle height=18><PARAM NAME="_cx" VALUE="1084"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/9.2`4.3/12,[1]{y`equal`1}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT> 에서의 <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=104 align=absMiddle height=18><PARAM NAME="_cx" VALUE="2751"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="4063280"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/23.4`4.3/12,[1]{x`equal`a (a`lt`0`rrbracket)}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT> 이고, i), ii)  식과 <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=12 align=absMiddle height=18><PARAM NAME="_cx" VALUE="317"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/2.8`4.3/12,[1]{y}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT> 축과의 교점의 좌표는 각각  <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=111 align=absMiddle height=18><PARAM NAME="_cx" VALUE="2936"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="4063280"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/25.2`4.3/12,[1]{-a`plus`1 , a`plus`1 }/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT>이다. ( <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=43 align=absMiddle height=18><PARAM NAME="_cx" VALUE="1137"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/9.7`4.3/12,[1]{a`lt`0}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT> 이므로 <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=110 align=absMiddle height=18><PARAM NAME="_cx" VALUE="2910"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="4063280"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/24.6`4.3/12,[1]{-a`plus`1`gt`a`plus`1}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT>) 따라서 둘러싸인 삼각형의 넓이는 <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=195 align=absMiddle height=35><PARAM NAME="_cx" VALUE="5159"><PARAM NAME="_cy" VALUE="926"><PARAM NAME="BackColor" VALUE="4063280"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/44`8.2/12,[1]{{-a}/{2}{*(-a`plus`1)-(a`plus`1)}`equal`4}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT> 이므로 <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=120 align=absMiddle height=28><PARAM NAME="_cx" VALUE="3175"><PARAM NAME="_cy" VALUE="740"><PARAM NAME="BackColor" VALUE="4063280"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/26.9`5.6/12,[1]{{a}^{2}`equal`4 , a`equal`+-`2}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT> <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=43 align=absMiddle height=18><PARAM NAME="_cx" VALUE="1137"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/9.7`4.3/12,[1]{a`lt`0}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT> 이므로 <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=53 align=absMiddle height=18><PARAM NAME="_cx" VALUE="1402"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/12`4.3/12,[1]{a`equal`-2}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT>

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