历年试题及答案
n
x n1 x x e 1 x x e limn nex 1 n 1 limnex n x e
n e
n
1 x x
1 x2ex 1lim n e
n x x2ex 1
lim
1 t t et 0t
nt
ln(1 t)01 t 1
0
t x2ex 1lim
t2 t 01
x2exlimt (1 t)ln(1 t)
t)t2
t 0(1 x2exlim
t (1 t)ln(1 t)
t 0t2
0
x2exlim
1 1 ln(1 t)
t 02t
x2ex。 2、求 1 x4 x8
x(1 x8)
dx.
: 1 x4 x811 x4 x8211 x2 x4
解x(1 x8)dx 2 x2(1 x8)dx 2 x(1 x4
)
dx 11 x2 x4211 x4 x2x2(1 x4)dx 4 x(1 x2)
dx 1 3
1 ABC 1 1
4 x 1 x x 1 dx 4 x 1dx x 1x
1 4 32ln(x 1) lnx 12ln(x 1)
C 38ln(x 1) 11
4lnx 8
ln(x 1) C.