数学分析I-14-期末复习题.pdf

555 I666 444 OOO 1 lim n n2 n n 2 lim n n 1 n 2 n 10 3 lim n 1 1 2 1 2 3 1 n n 1 4 lim n 1 2 3 22 2n 1 2n 5 lim n n 1 2n 3n 6 lim x 2 x2 x2 4 1 x 2 7 lim x 3x 1 2 x2 1 x 1 2x 1 3 8 lim x 0 xsin 1 x 1 x sinx 9 lim x x2arctanx 2x2 1 10 lim x 2 x2 ax b x2 3x 2 8 a b 11 lim x 4 1 2x 3 x 2 12 lim x 0 2 1 cosx 1 x2 1 13 lim x 0 x2sin 1 x sinx 14 lim x 0 p1 f x sinx 1 e3x 1 2 lim x 0 f x 15 lim x 0 ex 2 cos2x sinxln 1 x 16 lim x 0 1 xsinx cosx ex 2 1 17 lim x 0 1 x3 2 cosx 3 x 1 18 lim x 0 cosx 1 x2 19 lim x 0 1 2x 3 sin x 1 20 lim x 3x 2 3x 1 x 21 lim x 0 ax bx cx 3 1 x a 0 b 0 c 0 22 lim x 0 1 ln 1 x 2 x 23 lim x 0 cosx 1 ln 1 x2 24 lim x 0 tanx x ln 1 x2 25 lim x 0 1 x 1 ln 1 x 26 lim x x 1 x2 1 ln x 27 lim x x x 2 ln 1 1 x V 28 lim x x 4sinx 5x 2cosx 29 f x 3x0 f0 x0 1 1 lim x x0 f x0 M x f x0 M x 2 lim x x0 f x0 2sinx f x0 arctanx 30 f x vf 1 x af x f0 0 b f0 1 31 f x 3a k Y lim h 0 f a h f a h 2f a h2 1 y arcsin 1 x2 2 y cosnx sinnx 3 y ln x 1 x2 4 y arctan 1 x2 5 y tanx2 arctan2x 6 y e xsin 3 x 7 y aa x xx 2 8 x ln 1 t2 y arctant y y x dy dx d2y dx2 9 y xx 3x x3 ln 3 x ln3 dy 10 y sin 1 x2 dy 2 11 y ln cos2x 1 sin4 x dy 12 f x y xf 1 x y 0 y00 13 y sin 2x y n 14 y 1 x x 2 y n 15 y f x2 1 dy nnn 1 Rx2 sin2x x2sin2x dx 2 R x 1 2 x x2 1 dx 3 R x4 1 x2 dx 4 R 1 x2 2x 2dx 5 Rxtan 1 x2 1 x2dx 6 R 1 lnx x dx 7 R arctan xdx 8 R xearctanx 1 x2 3 2 dx 9 R 1 x2 1 x2 3 2 dx 10 R x3ex 2dx 11 Rlnsinx sin2x dx 12 Rarctanex e2x dx 13 R e2x 1 tanx 2dx 14 R xsin xdx 15 R 1 1 sinx cosxdx 16 Rxf x dx arcsinx c R 1 f x dx ooo nnn yyy 3 1 N y lim n n2 n2 4 1 2 an 1 1 22 1 32 1 n2 y lim n an 3 3 y lim x 1 x2 1 2x2 x 1 2 3 4 8B Ky lim x cosx 3 5 f3 0 vf x2 f x lim x 0 f x lim x f x f 1 y f x f 1 x 0 6 f x ex 1 x x 1 m 9a 7 f x 1 x sinx x 0 3x 0 Y a b 8 f3 0 Y v0 f x x x 0 a1 0 an 1 f an n 1 2 y 1 an 2 lim n an t Kf t t 9 e f x 3 a b Y f a f b k f0 a f 0 b 0 Kk a b f k 10 f x ax3 b x 0 1 1 x x 0 a b f x 3x 0 12 y x 0 ln x 1 arctanx 1 x 13 f x 3 0 1 Y 3 0 1 f 1 f 0 0 f 1 2 1 y 3 0 1 f0 1 14 k 0 k arctanx kx 0 3 15 f a b f a f b 0 3c a b f c 0 y 3