Ôn luyện 2019 môn toán

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Lê Phương Anh - Khuất Thị Thùy Linh

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Xin chân thành c̫P˯Q

MӨC LӨC

PHҪ1ĈҤI SӔ VÀ GIҦI TÍCH 1

Chӫ ÿӅ 1 MӋQKÿӅ , tұp hӧp, hàm sӕ 2

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Chӫ ÿӅ 4 Tә hӧp – ;iFVXҩt 76

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Chӫ ÿӅ 5 Dãy sӕ – *LӟLKҥn – Ĉҥo hàm 108

&KX\rQÿӅ 'm\Vӕ&ҩp sӕ cӝQJ– cҩp sӕ QKkQ  108 &KX\rQÿӅ *Lӟi hҥQGm\Vӕ  122 &KX\rQÿӅ *Lӟi hҥQKjPVӕ+jPVӕ OLrQWөc  129 &KX\rQÿӅ Ĉҥo hàm  141 &KX\rQÿӅ 3KѭѫQJWUuQKWLӃSWX\ӃQ  153

Chӫ ÿӅ 6 ӬQJGөQJÿҥRKjPÿӇ khҧRViWKjPVӕ 161

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&KX\rQÿӅ  &ӵFWUӏ cӫa hàm sӕ  175 &KX\rQÿӅ *LiWUӏ lӟQQKҩWJLiWUӏ QKӓ QKҩt cӫa hàm sӕ  191 &KX\rQÿӅ 7LӋm cұQFӫDÿӗ thӏ hàm sӕ  199 &KX\rQÿӅ Ĉӗ thӏ hàm sӕ  205

Chӫ ÿӅ 7 Hàm sӕ PNJKjPVӕ ORJDULWYjKjPVӕ ONJ\WKӯD 219

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Chӫ ÿӅ 1JX\rQKjP– Tích phân 261

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Chӫ ÿӅ 9 Sӕ phӭc 295

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PHҪN 2: HÌNH HӐC 315

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Chӫ ÿӅ 3KѭѫQJSKiSWӑDÿӝ WURQJPһt phҷQJ 335

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Chӫ ÿӅ 3KpSGӡLKuQKYjSKpSÿӗQJGҥQJWURQJPһt phҷQJ 359

&KX\rQÿӅ 3KpSELӃQKuQKSKpSWӏQKWLӃQ  359 &KX\rQÿӅ 3KpSÿӕi xӭQJWUөFÿӕi xӭQJWkP  365 &KX\rQÿӅ 3KpSTXD\YjSKpSGӡLKuQK  372 &KX\rQÿӅ 3KpSYӏ tӵSKpSÿӗQJGҥQJ  377

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Chӫ ÿӅ 7 MһWQyQPһWWUө, mһt cҫX 488

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Chӫ ÿӅ 3KѭѫQJSKiSWӑDÿӝ WURQJNK{QJJLDQ 520

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Cho hàm sӕ y f x [iFÿӏnh trên tұp K (K là khoҧQJÿRҥn hay nӱa khoҧng)

Hàm sӕ F x ÿѭӧc gӑi là nguyên hàm cӫa hàm sӕ y f x trên K nӃu

Ĉӏnh lí 1 NӃu F x là mӝt nguyên hàm cӫa hàm sӕ f x trên K thì vӟi mӛi hҵng sӕ C, e2x 2018x23x1 e 2x, vӟi mӑi x f f  ;

a b c

F F f

42

0

a

b C a

a b C

7DFy d 2 d 2

ln 2

x x

x

C



Lӡi giҧi chi tiӃt

11

Lӡi giҧi chi tiӃt

Cách 1: I ³x e d 2x xĈһt 2 1 2

2

x x

NӃu bұc cӫa P x lӟQKѫQEұc cӫa Q x thì ta thӵc hiӋQSKpSFKLDÿDWKӭc

NӃu bұc cӫa P x lӟQKѫQEұc cӫa Q x và Q x có dҥng tích nhiӅu nhân tӱ thì ta phân tích f x

thành tәng cӫa nhiӅu phân thӭc

P x A

P x B

P x C

3KѭѫQJSKiSJLҧi6ӱ dөQJSKѭѫQJSKiSÿәi biӃn sӕ, sӱ dөng vi phân

Mӝt sӕ dҥQJÿәi biӃn sӕ ÿһc biӋW

1

Ví dө 2: Tìm nguyên hàm

dx I

x C

2

cos

.2

x C

&kX TӕFÿӝ WKD\ÿәi doanh thu (bҵQJÿ{ODWUrQPӝt máy tính) cho viӋc bán x máy tính là f x ,

biӃt f xc 12x53x2 2x12 Tìm tәng doanh WKXNKLEiQÿѭӧFPѭӡLKDLPi\WtQKÿҫu tiên

&kX Mӝt bác thӧ [k\EѫPQѭӟc vào bӇ chӭDQѭӟc Gӑi h t là thӇ WtFKQѭӟFEѫPÿѭӧc sau t giây

Cho h tc 3at2 YjEDQÿҫu bӇ NK{QJFyQѭӟc Sau 5 giây thì thӇ WtFKQѭӟc trong bӇ là bt 150m , sau 3

10 giây thì thӇ WtFKQѭӟc trong bӇ là 1100m3 Tính thӇ tích cӫDQѭӟc trong bӇ VDXNKLEѫPÿѭӧc 20 giây

&+8<Ç1Ĉӄ 2

TÍCH PHÂN

A KIӂN THӬC TRӐNG TÂM

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Cho hàm sӕ y f x ...

PhҫQ+uQKKӑc

VӟLQKӳQJѭXÿLӇm ҩ\FK~QJW{LPRQJUҵQJ Ôn luyên thi tr̷c nghi͏m THPTQG mơn Tốn

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