f ( x ) = x ^{3} - 9 x ^{2} + 24 x + a

2a:["$","div",null,{"className":"math-text text-[15px] leading-[1.9]","children":[["$","p","p0-0",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["함수 ",["$","span","p0-0-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$9c"}}],"의 극댓값이 ",["$","span","p0-0-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

10

"}}],"일 때, 상수 ","$L9d","의 값은? [4점]\n① ","$L9e","\n② ","$L9f","\n③ ","$La0","\n④ ","$La1","\n⑤ ","$La2",""]}]]}] a3:T4b4,

\left\{ a _{n} \right\}

a4:T4fe,

a _{1} = 3

a5:Tf41,

\displaystyle 2 a _{n+1} = 3 a _{n} - \frac{6 n + 2}{( n + 1 ) !}

2b:["$","div",null,{"className":"math-text text-[15px] leading-[1.9]","children":[["$","p","p0-0",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["수열 ",["$","span","p0-0-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$a3"}}],"은 ",["$","span","p0-0-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$a4"}}],"이고,\n\t\t",["$","span","p0-0-t0-m5",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$a5"}}]," (","$La6",")\n을 만족시킨다. 다음은 일반항 ","$La7","을 구하는 과정이다."]}],"$La8","$La9"]}] aa:Ta59,

\displaystyle \mathrm{\overline{A _{1} D _{1}}} = 2

ab:Ta59,

\displaystyle \mathrm{\overline{A _{1} B _{1}}} = 1

2c:["$","div",null,{"className":"math-text text-[15px] leading-[1.9]","children":[["$","p","p0-0",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["그림과 같이 ",["$","span","p0-0-t0-m1",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$aa"}}],", ",["$","span","p0-0-t0-m3",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$ab"}}],"인 직사각형 ","$Lac","에서 선분 ","$Lad","의 중점을 ","$Lae","이라 하자. 중심이 ","$Laf",", 반지름의 길이가 ","$Lb0","이고 중심각의 크기가 ","$Lb1","인 부채꼴 ","$Lb2","을 그리고, 부채꼴 ","$Lb3","에 색칠하여 얻은 그림을 ","$Lb4","이라 하자. 그림 ","$Lb5","에서 부채꼴 ","$Lb6","의 호 ","$Lb7","이 선분 ","$Lb8","과 만나는 점을 ","$Lb9","라 하고, 중심이 ","$Lba",", 반지름의 길이가 ","$Lbb","인 원이 선분 ","$Lbc","과 만나는 점을 ","$Lbd","라 하자. 가로와 세로의 길이의 비가 ","$Lbe","이고 가로가 선분 ","$Lbf","과 평행한 직사각형 ","$Lc0","를 그리고, 직사각형 ","$Lc1","에서 그림 ","$Lc2","을 얻는 것과 같은 방법으로 만들어지는 부채꼴에 색칠하여 얻은 그림을 ","$Lc3","라 하자.\n이와 같은 과정을 계속하여 ","$Lc4","번째 얻은 그림 ","$Lc5","에 색칠되어 있는 부분의 넓이를 ","$Lc6","이라 할 때, ","$Lc7","의 값은? [4점]"]}],"$Lc8","$Lc9","$Lca","$Lcb"]}] cc:T4a2,

A ^{2} = - A

cd:T8c8,

A ^{2} + B ^{2} = A + E

2d:["$","div",null,{"className":"math-text text-[15px] leading-[1.9]","children":[["$","p","p0-0-0",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["두 이차정사각행렬 ",["$","span","p0-0-0-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

A

"}}],", ",["$","span","p0-0-0-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

B

"}}],"가\n\t\t",["$","span","p0-0-0-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$cc"}}],", ",["$","span","p0-0-0-t0-m7",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$cd"}}],"\n를 만족시킬 때, <보기>에서 옳은 것만을 있는 대로 고른 것은? (단, ","$Lce","는 단위행렬이다.) [4점]"]}],"$Lcf","$Ld0"]}] d1:T558,

0 < a < 1 < b

d2:T822,

f ( x ) = \log _{a} ( bx - 1 )

2e:["$","div",null,{"className":"math-text text-[15px] leading-[1.9]","children":[["$","p","p0-0",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["",["$","span","p0-0-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$d1"}}],"인 두 실수 ",["$","span","p0-0-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

a

"}}],", ",["$","span","p0-0-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

b

"}}],"에 대하여 두 함수\n\t",["$","span","p0-0-t0-m7",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$d2"}}],", ","$Ld3","\n이 있다. 곡선 ","$Ld4","와 ","$Ld5","축의 교점이 곡선 ","$Ld6","의 점근선 위에 있도록 하는 ","$Ld7","와 ","$Ld8"," 사이의 관계식과 ","$Ld9","의 범위를 옳게 나타낸 것은? [4점]\n① ","$Lda"," (","$Ldb",")\n② ","$Ldc"," (","$Ldd",")\n③ ","$Lde"," (","$Ldf",")\n④ ","$Le0"," (","$Le1",")\n⑤ ","$Le2"," (","$Le3",")"]}]]}] e4:Tefc,

\displaystyle \lim\limits _{x \rightarrow n} \frac{f ( x )}{g ( x )} = ( n - 1 ) ( n - 2 )

2f:["$","div",null,{"className":"math-text text-[15px] leading-[1.9]","children":[["$","p","p0-0",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["최고차항의 계수가 ",["$","span","p0-0-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

1

"}}],"인 두 삼차함수 ",["$","span","p0-0-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

f ( x )

"}}],", ",["$","span","p0-0-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

g ( x )

"}}],"가 다음 조건을 만족시킨다."]}],["$","p","p0-1",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":[" (가) ",["$","span","p0-1-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

g ( 1 ) = 0

"}}],"\n (나) ",["$","span","p0-1-t0-m3",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$e4"}}]," (","$Le5",", ","$Le6",", ","$Le7",", ","$Le8",")"]}],"$Le9"]}] ea:Te01,

\displaystyle \lim\limits _{n \rightarrow \infty} \frac{3 n ^{2} + 5}{n ^{2} + 2 n}

30:["$","div",null,{"className":"math-text text-[15px] leading-[1.9]","children":[["$","p","p0-0",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["",["$","span","p0-0-t0-m1",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$ea"}}],"의 값을 구하시오. [3점]"]}]]}] eb:T7ad,

f ( x ) = x ^{2} + x + 3

ec:T43c,

f' ( 10 )

31:["$","div",null,{"className":"math-text text-[15px] leading-[1.9]","children":[["$","p","p0-0",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["함수 ",["$","span","p0-0-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$eb"}}],"에 대하여 ",["$","span","p0-0-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$ec"}}],"의 값을 구하시오.\n[3점]"]}]]}] ed:T534,

f ( x ) = 2 ^{x}

ee:Ta19,

\displaystyle g ( x ) = \left( \frac{1}{2} \right) ^{2x}

32:["$","div",null,{"className":"math-text text-[15px] leading-[1.9]","children":[["$","p","p0-0",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["닫힌 구간 ",["$","span","p0-0-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

[ - 1 , 3 ]

"}}],"에서 두 함수\n\t\t",["$","span","p0-0-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$ed"}}],", ",["$","span","p0-0-t0-m5",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$ee"}}],"\n의 최댓값을 각각 ","$Lef",", ","$Lf0","라 하자. ","$Lf1","의 값을 구하시오. [3점]"]}]]}] f2:T4b4,

\left\{ a _{n} \right\}

f3:T501,

a _{1} = 15

f4:Tfeb,

\displaystyle \sum\limits _{k = 1} ^{n} \left( a _{k + 1} - a _{k} \right) = 2 n + 1

33:["$","div",null,{"className":"math-text text-[15px] leading-[1.9]","children":[["$","p","p0-0",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["수열 ",["$","span","p0-0-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$f2"}}],"은 ",["$","span","p0-0-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$f3"}}],"이고,\n\t\t",["$","span","p0-0-t0-m5",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$f4"}}]," (","$Lf5",")\n을 만족시킨다. ","$Lf6","의 값을 구하시오. [4점]"]}]]}] f7:T629,

y = - x ^{3} + 2 x

34:["$","div",null,{"className":"math-text text-[15px] leading-[1.9]","children":[["$","p","p0-0",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["곡선 ",["$","span","p0-0-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$f7"}}]," 위의 점 ",["$","span","p0-0-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

( 1 , 1 )

"}}],"에서의 접선이 점\n",["$","span","p0-0-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

( - 10 , a )

"}}],"를 지날 때, ","$Lf8","의 값을 구하시오. [4점]"]}]]}] f9:T7c5,

\left( x _{n} , y _{n} \right)

fa:T995,

( x _{1} , y _{1} ) = ( 1 , 1 )

35:["$","div",null,{"className":"math-text text-[15px] leading-[1.9]","children":[["$","p","p0-0",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["자연수 ",["$","span","p0-0-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

n

"}}],"에 대하여 순서쌍 ",["$","span","p0-0-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$f9"}}],"을 다음 규칙에 따라 정한다."]}],["$","p","p0-1",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":[" (가) ",["$","span","p0-1-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$fa"}}],"\n (나) ","$Lfb","이 홀수이면 ","$Lfc","이고,\n ","$Lfd","이 짝수이면 ","$Lfe","이다."]}],"$Lff"]}] 36:["$","div",null,{"className":"math-text text-[15px] leading-[1.9]","children":[["$","p","p0-0",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["양수 ",["$","span","p0-0-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

x

"}}],"에 대하여 ",["$","span","p0-0-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

\\log x

"}}],"의 가수를 ",["$","span","p0-0-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

f ( x )

"}}],"라 하자. 다음 조건을 만족시키는 두 자연수 ",["$","span","p0-0-t0-m7",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

a

"}}],", ",["$","span","p0-0-t0-m9",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

b

"}}],"의 모든 순서쌍 ",["$","span","p0-0-t0-m11",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

( a , b )

"}}],"의 개수를 구하시오. [4점]"]}],"$L100"]}]

2014년-06월-고3-수리(A형)