东南大学2013-14-2高数(B,I)期中试卷分析.pdf

2013p B I November 18 2013 euy s 1 s K W K K 7 K 11 K8 Kz K4 32 1 f x 1 e x 1 x 1 m 0 0 0 1 1 1 O 111 aaa aaa m 111 aaa m 2 f x 1 3x 2 ln 1 x x 0 acos x x 0 3 x 0 Y Ka e6e6e6 3 4 lim x r x q 2x 3x x 2 2 2 2 2 2 4 y arcsine2x Kdy 2e2x 1 e4xdx 2e2x 1 e4xdx 2e2x 1 e4xdx 5 x 0 ex esin x xn d Kn 3 3 3 a 1 6 1 6 1 6 6 f x x2ln 1 x K f 5 0 40 4040 7 y y x d y yex 2eysin x 7x 2 Ky0 0 e 4e 4e 4 O e K K 4 K z K8 32 1 y x x2 2 x 1 2 y0 x y0 x x x2 2 x 1 2 1 x x x2 2 2 x 1 2 x2 x 1 x 1 3 x2 2 y0 x x x2 2 x 1 2 1 x x x2 2 2 x 1 2 x2 x 1 x 1 3 x2 2 y0 x x x2 2 x 1 2 1 x x x2 2 2 x 1 2 x2 x 1 x 1 3 x2 2 2 O 4 lim x 0 2sin2x x3cos 1 x 1 xsin x 1 cos x 4 1 1 lim x 0 2sin2x x3cos 1 x 1 xsin x 1 cos x lim x 0 1 1 xsin x lim x 0 2sin2x x3cos 1 x 1 cos x lim x 0 1 1 xsin x lim x 0 2sin2x x3cos 1 x 1 cos x lim x 0 1 1 xsin x lim x 0 2sin2x x3cos 1 x 1 cos x lim x 0 2sin2x x3cos 1 x x2 2 4lim x 0 sin2x x2 2lim x 0 xcos 1 x 4lim x 0 2sin2x x3cos 1 x x2 2 4lim x 0 sin2x x2 2lim x 0 xcos 1 x 4lim x 0 2sin2x x3cos 1 x x2 2 4lim x 0 sin2x x2 2lim x 0 xcos 1 x 4 3 O 4 lim n n 1 n2 nsin1 n 2 n2 nsin2 n n n2 nsinn P xn n 1 n2 nsin1 n 2 n2 nsin2 n n n2 nsinn Kyn n2 n n 1 2 n2 n xn n2 n n 1 2 n2 n zn lim n yn lim n zn 3 2 dY n lim n n 1 n2 nsin1 n 2 n2 nsin2 n n n2 nsinn 3 2 lim n n 1 n2 nsin1 n 2 n2 nsin2 n n n2 nsinn 3 2 lim n n 1 n2 nsin1 n 2 n2 nsin2 n n n2 nsinn 3 2 4 f x 1 x 1 ex 1 x 0 1 2 x 0 3 x 0 Y5 5 e f 0 0 P99SKl18K n K 8 L x cost y sint tcost 1 L3t 4 A 2 O d2y dx2 dy dx t 4 t 2cott t 4 4 2 2 2 2 2 1 4 y 4 2 x 3 2 2 y 4 2 x 3 2 2 y 4 2 x 3 2 2 d2y dx2 1 sint 2 sin3t d2y dx2 1 sint 2 sin3t d2y dx2 1 sint 2 sin3t o K 7 f x xsin x kLagrange 4 Maclaurin f x x2 x4 6 6cos x xsin x 6 x6 0 1 f x x2 x4 6 6cos x xsin x 6 x6 0 1 f x x2 x4 6 6cos x xsin x 6 x6 0 1 5sin x xcos x 5 x5 0 1 5sin x xcos x 5 x5 0 1 5sin x xcos x 5 x5 0 0 i 1 2 n y xn yyy xn 1 xn an 1 1 a1 1 an 1 0 xn N4O q xn 1 1 1 a1 1 1 a1 1 1 a1 1 a2 1 1 a1 1 a2 1 1 a1 1 a2 1 a3 1 1 a1 1 an 1 1 1 a1 1 an 1 1 1 a1 1 an 1 xn k xn K 6 f x 3 a b Y 3 a b S f a f b 0 f 0 c 0 a c b y f c 0 abc A B C x y 0 x Figure 1 1 K yyy f a