1 함수와 극한 / 1
1.1 함수와 그 표현 ······················································1
1.2 필수적인 함수 목록 ··············································11
1.3 함수의 극한 ···························································26
1.4 극한 셈 ···································································38
1.5 연속 ········································································49
1.6 무한대와 관련된 극한 ··········································61
1 복습 ············································································75
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2 도함수 / 79
2.1 미분 계수와 변화율 ·············································79
2.2 도함수 ····································································90
2.3 기본적인 미분법 ···················································102
2.4 곱과 몫의 미분법 ··················································114
2.5 연쇄 법칙 ·······························································122
2.6 음함수의 미분법 ···················································131
2.7 서로 관련된 변화율 ··············································137
2.8 선형 근사와 미분 ··················································144
2 복습 ············································································150
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3 역함수: 지수․로그․역삼각 함수 / 155
3.1 지수 함수 ·······························································155
3.2 역함수와 로그 ·······················································161
3.3 로그 함수와 지수 함수의 도함수 ·······················174
3.4 지수적 증가와 감소 ··············································182
3.5 역삼각 함수 ···························································190
3.6 쌍곡선 함수 ···························································196
3.7 부정형과 로피탈의 법칙 ······································203
3 복습 ············································································211
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4 미분의 활용 / 215
4.1 최댓값과 최솟값 ···················································215
4.2 평균값 정리 ···························································223
4.3 도함수와 그래프의 모양 ······································230
4.4 곡선 그리기 ···························································239
4.5 최적화 문제 ···························································247
4.6 뉴턴의 방법 ···························································259
4.7 역도함수 ································································265
4 복습 ···········································································272
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5 적분 / 276
5.1 넓이와 거리 ··························································276
5.2 정 적분 ··································································289
5.3 정 적분의 값 찾기 ···············································303
5.4 미적분학의 기본 정리 ·········································314
5.5 치환 적분법 ··························································324
5 복습 ···········································································332
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