《01第12-19届北京市大学生数学竞赛全部试题解答》.pdf

2000 10 14 9:00~11:30 .. 20 9:30 a tan x +b(1−cos x) 1lim 2 a 2 = . x →0 ln(1−2x) +c (1−e−x ) 2 ∂ z 2 0 x 0 z sin y y 0 z sin x z = . x y ∂∂ ∞ n +1 3∑ = . n 0 n ! ∞ ∞ 4∑a (x +1)n (−4, 2) ∑na (x −3)n . n n n 0 n 0 1 1 1 2 ( ) 5 tdt e x dx = . ∫ ∫ 0 t 1 6y 1,y ex , y 2ex , y ex + π . 1 1 1 n 7 x n x n + = . { } sin ( 2) sin lim ∑x n n k n +1 n +1 n→∞ n +1 k 1 cos x −1 8f (x ) x 0 lim f (x ) 1f ′(0) = . x →0 e −1 1 9 x ≠0 ′ = . f (x ) ∫f (t x )dt f (x ) +x sin x , f (0) 0 f (x ) 0 10 C x 2 +y 2 +z 2 a2 x 2 +y 2 +z 2 b2 3