[
绗?/p>
1
椤?
鍏?/p>
3
椤?/p>
]
xxxx
澶у
绗竴瀛︽湡鏈熸湯鑰冭瘯璇曞嵎
璇剧▼鍚嶇О锛?/p>
Calculus (I)
Problem 1(
3
脳
5=15pts.)Fill in the blank of each unfinished statement such that it
is right. Mark your answer on the answer sheet.
(1)
2
lim
(
2
)
x
x
x
x
飩�偉
飥?
飥?/p>
飥?/p>
.
(2)
If
0
lim[
(
)
(
)]
2
x
f
x
g
x
飩?/p>
飥?/p>
飥?/p>
and
0
lim[
(
)
(
)]
1
x
f
x
g
x
飩?/p>
飥?/p>
飥?/p>
, then
0
lim
(
)
(
)
x
f
x
g
x
飩?/p>
飥?/p>
.
(3)
1
2
4
1
sin
(
1
)
1
x
x
dx
x
飥?/p>
飥?/p>
飥?
飥?/p>
飥?/p>
飪?
.
(4) Let
1
sin
if
0
(
)
0
if
0
x
x
f
x
x
x
飪?
飩?/p>
飪?/p>
飥?/p>
飪?/p>
飪?/p>
飥?/p>
飪?/p>
. Then
(
)
f
x
飩?/p>
飥?/p>
.
(5)
1
1
x
dx
x
飥?/p>
飥?/p>
飥?/p>
飪?
.
Problem
2(
3
脳
5=15pts.)For
each
blank
in
the
following
statement,
choose
the
best answer from the choice given below. Mark your choice on the answer sheet.
(6)
If
)
(
x
f
is differentiable at
0
飥?/p>
x
such that
0
)
0
(
飥?/p>
f
and
(0)
1
f
飩?/p>
飥?/p>
, then
x
x
f
x
f
x
)
3
(
)
2
(
lim
0
飥?/p>
飩?/p>
=________
.
A.0
B.1
C.3
D.5
(7)
Let
(
)
f
飪?/p>
be a differentiable function. Then
(
)
(
)
f
x
d
f
e
dx
飥?/p>
________.
A.
(
)
(
)
(
)
(
)
f
x
f
x
e
f
x
f
e
飩?/p>
飩?/p>
B.
(
)
(
)
(
)
(
)
f
x
f
x
e
f
x
f
e
飩?/p>
飩?/p>
飩?/p>
C.
(
)
(
)
(
)
f
x
f
x
f
e
飩?/p>
飩?/p>
D.
(
)
(
)
(
)
f
x
f
x
e
f
e
飩?/p>
飩?/p>
(8)
飥?/p>
飪?/p>
飪?
飪?
飪?/p>
飪?/p>
飪?/p>
飥?
飩?/p>
x
x
x
1
0
7
1
lim
________.
A.
7
1
e
B.
7
1
飥?/p>
e
C.
7
e
D.
7
飥?/p>
e
(9)
If
f
and
g
are continuous and
(
)
(
)
f
x
g
x
飩?/p>
for
a
x
b
飩?/p>
飩?/p>
, then