Sec 17

eu du = eu + c. sen u du = − cos u + c. cos u du = sen u + c. tg u du = ln |sec u| + c. cotg u du = ln |sen u| + c. sec u du = ln |sec u + tg u| + c. cosec u du = ln |cosec u − cotg u| + c. sec u tg u du = sec u + c. cosec u cotg u du = −cosec u + c. sec2 u du = tg u + c. cosec2 u du = −cotg u + c. 1 du = a arc tg u + c. a u2 +a2 du u2 −a2 1 = 2a ln √ du u2 +a2 √ du u2 −a2 √ du = arc sen u + c, a a2 −u2 1 √ du = a arc sec u a u u2 −a2 Sejam u e v fun¸˜es deriv´veis de x e n conco a…

eu du = eu + c. sen u du = − cos u + c. cos u du = sen u + c. tg u du = ln |sec u| + c. cotg u du = ln |sen u| + c. sec u du = ln |sec u + tg u| + c. cosec u du = ln |cosec u − cotg u| + c. sec u tg u du = sec u + c. cosec u cotg u du = −cosec u + c. sec2 u du = tg u + c. cosec2 u du = −cotg u + c. du 1 = a arc tg u + c. a u2 +a2 du u2 −a2 1 = 2a ln √ du u2 +a2 √ du u2 −a2 √ du = arc sen u + c, a a2 −u2 1 √ du = a arc sec u a u u2 −a2 Sejam u e v fun¸˜es deriv´veis de x e n conco a…

eu du = eu + c. sen u du = − cos u + c. cos u du = sen u + c. tg u du = ln |sec u| + c. cotg u du = ln |sen u| + c. sec u du = ln |sec u + tg u| + c. cosec u du = ln |cosec u − cotg u| + c. sec u tg u du = sec u + c. cosec u cotg u du = −cosec u + c. sec2 u du = tg u + c. cosec2 u du = −cotg u + c. du 1 = a arc tg u + c. a u2 +a2 du u2 −a2 1 = 2a ln √ du u2 +a2 √ du u2 −a2 √ du = arc sen u + c, a a2 −u2 1 √ du = a arc sec u a u u2 −a2 Sejam u e v fun¸˜es deriv´veis de x e n conco a…

eu du = eu + c. sen u du = − cos u + c. cos u du = sen u + c. tg u du = ln |sec u| + c. cotg u du = ln |sen u| + c. sec u du = ln |sec u + tg u| + c. cosec u du = ln |cosec u − cotg u| + c. sec u tg u du = sec u + c. cosec u cotg u du = −cosec u + c. sec2 u du = tg u + c. cosec2 u du = −cotg u + c. du 1 = a arc tg u + c. a u2 +a2 du u2 −a2 1 = 2a ln √ du u2 +a2 √ du u2 −a2 √ du = arc sen u + c, a a2 −u2 1 √ du = a arc sec u a u u2 −a2 Sejam u e v fun¸˜es deriv´veis de x e n conco a…

eu du = eu + c. sen u du = − cos u + c. cos u du = sen u + c. tg u du = ln |sec u| + c. cotg u du = ln |sen u| + c. sec u du = ln |sec u + tg u| + c. cosec u du = ln |cosec u − cotg u| + c. sec u tg u du = sec u + c. cosec u cotg u du = −cosec u + c. sec2 u du = tg u + c. cosec2 u du = −cotg u + c. du 1 = a arc tg u + c. a u2 +a2 du u2 −a2 1 = 2a ln √ du u2 +a2 √ du u2 −a2 √ du = arc sen u + c, a a2 −u2 1 √ du = a arc sec u a u u2 −a2 Sejam u e v fun¸˜es deriv´veis de x e n conco a…

9. y = sen u ⇒ y = u cos u. 10. y = cos u ⇒ y = −u sen u. 11. y = tg u ⇒ y = u sec2 u. 12. y = cotg u ⇒ y = −u cosec2 u. 13. y = sec u ⇒ y = u sec u tg u. 14. y = cosec u ⇒ y = −u cosec u cotg u. u 15. y = arc sen u ⇒ y = √1−u2 . 16. y = arc cos u ⇒ y = √−u 2 . 1−u u tg u ⇒ y = 1+u2 . −u cot g u ⇒ 1+u2 . 17. y = arc 18. y = arc 19. y = arc sec u, |u| 1 u ⇒ y = |u|√u2 −1 , |u| > 1. 20. y = arc cosec u, |u| 1 −u ⇒ y = |u|√u2 −1 , |u| > 1. • 1. 2.…

2x) 5.4. c‚s 2x = (1 – sen2x) 5.5. . tg 2x = 6. ExpressÑes para qualquer Triangulo 6.1. Lei do cosseno: 2bc.cos ‚ 6.2. Lei do seno: 6.3. Area: Rad 0 Grau 0„ 30„ 45„ 60„ 90„ 180„ 270„ Sen 0 1 0 -1 Cos 1 0 -1 0 Tg 0 1 0 Cotg 1 0 0 Sec 1 2 -1 Cosec 2 -1 -1 ÖLGEBRA 1. FÄrmula Binomial Onde n … positivo e 2. Produtos NotÜveis: 2.1 (x + y)2 = x2 + 2xy + y2 2.2 (x – y)2 = x2 – 2xy + y2 2.3 (x + y)3 = x3+3x2y + 3xy2 + y3 2.4 (x – y)3 = x3 – 3x2y + 3xy2 – y3 2.5 x2 – y2 = (x

eu + c. sen u d u = − cos u + c. cos u d u = sen u + c. tg u d u = ln |sec u| + c. cotg u d u = ln |sen u| + c. sec u d u = ln |sec u + tg u| + c. cosec u d u = ln |cosec u − cotg u| + c. sec u tg u d u = sec u + c. cosec u cotg u d u = −cosec u + c. sec2 u d u = tg u + c. cosec2 u d u = −cotg u + c. 1 du = a ar c tg u + c. a u2 +a2 du u2 −a2 1 = 2a ln √ du u2 +a2 √ du u2 −a2 √ du = ar c sen u + c, a a2 −u2 1 √du = a ar c sec u a u u2 −a2 Sejam u e v fun¸˜es deriv´veis de x e n conco…

(x ) g' (x ) dx 20 d 1 arc sen ( x ) = dx 1− x2 d 1 arc cos( x ) = − dx 1− x2 d 1 arc tg ( x ) = dx 1+ x2 d 1 arc cos sec( x ) = − dx x x2 −1 d 1 arc sec( x ) = dx x x 2 −1 d 1 arc cot g ( x ) = − dx 1+ x2 d senh ( x ) = cosh( x ) dx d cosh( x ) = senh ( x ) dx d tgh ( x ) = sec h 2 ( x ) dx d cos sec h ( x ) = − cos sec h ( x ) cot gh ( x ) dx d sec h ( x ) = − sec h ( x ) tgh ( x ) dx 3 21 4 22 5 23 6 d  f (x )  f ' (x ) g(x ) − f (x ) g' (x ) = dx …

Seja α = 111.371◦ e β = 37◦ 28 17 . 1 Converta α para o sistema GMS. Aproxime sua resposta para o segundo mais pr´oximo. 2 Converta β para graus. Aproxime sua resposta para o mil´esimo de grau mais pr´oximo. 3 Esboce α e β. 4 Encontre o suplementar de α. 5 Encontre o complementar de β. Exerc´ıcios Respostas 1 α ≈ 111◦ 22 16 2 β ≈ 37.471◦ 3 ˆ Angulo α ˆ Angulo β 4 θ = 180◦ − α = 180◦ − 111.371◦ = 68.629◦ 5 γ = 90◦ − 37◦ 28 17 = 89◦ 59 60 − 37◦ 28 17 = 52◦ 31 43 ˆ…