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电大江西广播电视大学《高等数学 B1》期末复
习题及参考答案
试卷代号：6450
江西广播电视大学《高等数学 B1》复习题 一、 填空题 1、
（比较大小）。
2、，
=
。
3、曲线的极值点是
。
4、
。
5、=
6、
。
（比较大小）。
7、，
9、
=
8、曲线的极值点是
。
。
10、=
。
11、设 ，则=
。
． 12、设设函数，则=
13、 =
。
14、函数的间断点是
。
15、设曲线在点 M 处的切线的斜率为 3，则点 M 的坐标为
。
16、函数在区间上单调
17、若存在原函数，则
18、设函数，则的定义域为
。
。
。
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19、函数与函数为
函数。
20、=
。
21、在上最大值为 3，最小值为 1，则取值范围是
。
22、 ， 则=
24、=
23、
。
。
25、若，则
。
二、 单项选择题 1、设的定义域为，则的定义域为(
).
A、
B、
B、 ；
C、
D、 2、设是的一个原函数，则等式（ ）
成立． A、 ；
C、 ；
D、 3、下列极限存在的有（
）.
A、
C、
B、
D、 4、=(
) A、
B、 C、
B、 C、
D、 5、当 _→0 时，
D、 6、在上有定
（
）为无穷小量 A、
).
义（），则 为(
A、偶函数
B、奇函数
C、非奇非偶函数
B、连续点；
D、单调函数 7、
设，则是的（ ）． A、驻点；
C、第一类间断点；
D、第二类间断点 8、若=，则在其定义域上是（
A、单调下降函数 B、凸函数（或下凹函数）
C、凹函数（或上凹函数） D、单调上升函数 9、=(
）.
) A、
B、 C、
D、 10、当时，（
B、2 C、
）
A、1
D、 11、设函数，则函数的图形关于
（
）对称．
A.
B.
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轴 C.
轴
D.
坐标原点 12、当时，比较是（
A 较高阶无穷小量
）
B 较低阶的无穷小量 C 等价无穷小量
D 同阶但不等价无穷小量 13、函数的反函数是（
）
A．
A．
B．
C．
D． 14、当时，下列变量中，无穷大量是
（
（
）
B．
B．
C．
D． 15、设在点处可导，则
）
A.
C．
D． 16、满足方程的点是函数的（
）
A．极大值点
B．极小值点
）
C．驻点
D．间断点
17、
设，则（
A.
B.
C.
D.
18、 （
）
A.
B.
1
C.
-1
D．e 19、设,则的值是（
A.
）
-1
1
B.
C.
D.
-2
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2 20、设，则=（
）
A.
B.
C.
D． 21、的定义域是是（ ）．
A、
C、
B、
D、 22、函数的反函数是（ ）． A、
B、
C、
D、 23、函数在区间内满足（ ）．
A、 先单调上升再单调下降
B、 单调上升
) A、 B、 C、
C、 先单调下降再单调
D、 25、
上升
（
D、 单调下降 24、=(
）。
A、1
B、0
C、
D、 三、计算题 1、设，求 2、 3、 4、，
求 5、 6、 7、设，求 8、 9、.计算 10、， 求 11、 12、计算 13、。
14、求 15、设，求。
16、设，求． 17、。
18、。
19、。
20、求曲线围成图形的面积。
21、 22、， 求 23、 ，求 24、求时的最大值、最小值。
25、 26、 四、证明题 1、证明：方程 时至少有一实根。
2、证明：
3、证明：当时，。
4、证明：当时 ，恒等式 成立。
5、证明：奇函数乘奇函数为偶函数。
江西广播电视大学 《高等数学 B1》复习题参考答案 一、填空题 1、＞
2、
3、
4、0
5、1 6、＞
13、 1
7、
8、
9、0
16、上升
10、 11、
12、 0
14、 15、(1，0)
17、
18、 19、同一（或相等、相同）
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20、 1 21、 22、 23、 24、0 25、 二、单项选择
题 1、A 2、B 3、B 4、D 5、D 6、A 7、C 8、C
9、D 10、B 11、B 12、A
13、D 14、C 15、C 16、C
18、A 19、B 20、A 21、D 22、C 23、C
8、 9、 10、 11、 12、
17、D
24、D 25、D 三、计算题 7、
13、解：.
14、解：
15、解：
故
16、解: 17、解：
= 18．解：
19、解：
= 20、解：所求平面图形如图阴影部分所示，由方程组
解出，设所求面积为，则有
1 o -1 y _ 4
21、
或 22、 23、 24、 令 得驻点 且是不可导点
计算得，，， 故 2 26、 四、证明题 1、证明：
在上连续，根据闭区间上连续函数零点定理，在上至少有一实零点。即时至
少有一实根。
2、证明：
3、证明: 令，有
当 时，，单增，且
故 时， ，即 。
4、证明: 5、证明：设为奇函数，即，
为偶函数， 故 奇函数乘奇函数为偶函数。
令 ， 那么由 ， 知
请您删除一下内容，O(∩_∩)O 谢谢！！！20__年中央电大期末复习考试小
抄大全，电大期末考试必备小抄，电大考试必过小抄 After earning his spurs
in the kitchens of The Westin, The Sheraton, Sens on the Bund, and a
sprinkling of other -notch venues, Simpson Lu fi nally got the chance to
bee his own boss in November 2021.
Sort of.
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The Shanghai-born chef might not actually own California Pizza
Kitchen (CPK) but he is in sole charge of both kitchen and frontof-
house at this Sinan Mansions＇stalwart. “It’s certainly a
responsibility to be the head chef, and then to have to manage the rest
of the restaurant as well,“ the 31-year-old tells Enjoy Shanghai.
“In hotels, for e_le, these jobs are strictly demarcated, so it’s
a great opportunity to learn how a business operates across the
board.“ It was a task that management back in sunny California
evidently felt he was ready for, and a vote of confi dence from a pany
that, to date, has opened 250 outlets in 11 countries.
And for added pressure, the Shanghai branch was also CPK’s China
debut. “For sure it was a big step, and unlike all their other Asia
operations that are franchises, they decided to manage it directly to
begin with,“ says Simpson. Two years ago a private franchisee took
over the lease, but the links to CPK headquarters are still strong, with
a mainland-based ＇brand ambassador’ on hand to ensure the business
adheres to its ethos of creating “innovative, hearth-baked pizzas“, a
slice of PR blurb that Simpson insists lives up to the hype. “They
are very innovative,“ he says.
“The problem with most fast food places is that they use the same
sauce on every pizza and just change the pings.
Every one of our 16 pizza sauces is a unique recipe that has been
formulated to plement the pings perfectly.“ The largely local
customer base evidently agrees and on Saturday and Sunday, at least, the
place is teeming.
The kids-eat-for-free policy at weekends is undoubtedly a big draw,
as well as is the spacious second-fl oor layout overlooked by a canopy
of green from Fu_ing Park over the road. The pany is also focusing on
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increasing brand recognition and in recent years has taken part in
outside events such as the regular California Week.
Still, the sta are honest enough to admit that business could be
better; as good, in fact, as in CPK’s second outlet in the popular
Kerry Parkside shopping mall in Pudong. “Sinan Mansions has really
struggled to get the number of visitors that were envisaged when it
first opened, and it hasn’t been easy for any of the tenants
here,“ adds Simpson.
“We’re planning a third outlet in the city in 20__, and we will
probably choose a shopping mall again because of the better foot
traffic.“ The tearooms once frequented by Coco Chanel and Marcel Proust
are upping sticks and ing to Shanghai, _u Junqian visits the Parisian
outpost with sweet treats.
One thing the century-old Parisian tearoom Angelina has shown is
that legendary fashion designer Coco Chanel not only had style and
glamor but also boasted great taste in food, pastries in particular.
One of the most popular tearooms in Paris, Angelina is famous for
having once been frequented by celebrities such as Chanel and writer
Marcel Proust.
Now Angelina has packed up its French ambience, efficient service,
and beautiful, forting desserts and flown them to Shanghai.
At the flagship dine-in and take-out space in Shanghai, everything
mimics the original tearoom designed from the beginning of the 20th
century, in Paris, the height of “Belle Epoque“.
The paintings on the wall, for e_le, are e_actly the same as the
one that depicts the landscape of southern France, the hometown of the
owner; and the small tables are intentional imitations of the ones that
Coco Chanel once sat at every afternoon for hot chocolate.
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The famous hot chocolate, known as L’Africain, is a lu_urious
mi_ture of four types of cocoa beans imported from Africa, blended in
Paris and then shipped to Shanghai.
It’s sinfully sweet, rich and thick as if putting a bar of melting
chocolate directly on the tongue and the fresh whipped cream on the side
makes a light, but equally gratifying contrast.
It is also sold in glass bottles as takeaway.
The signature Mont-Blanc chestnut cake consists of three parts: the
pureed chestnut on , the vanilla cream like stuffing, and the meringue
as base.
Get all three layers in one scoop, not only for the different
te_tures but also various flavors of sweetness.
The dessert has maintained its popularity for a century, even in a
country like France, perhaps the world’s most petitive place for
desserts.
A much overlooked pairing, is the Paris-New York chou_ pastry and
N226 chocolate flavored tea.
The chou_ pastry is a mouthful of airy pecan-flavored whipped cream,
while the tea, a blend of black teas from China and Ceylon, cocoa and
rose petals, offers a more subtle fragrance of flowers and chocolate.
Ordering these two items, featuring a muted sweetness, makes it
easier for you to fit into your little black dress.
Breakfast, brunch, lunch and light supper are also served at the
tearoom, “a hub of many cultures“ and takes in “a mi_ of different
styles of French cuisines“, according to the management team.
The semi-cooked foie gras terrine, is seductive and deceptive.
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It’s generously served at the size and shape of a toast, while the
actual brioche toast is baked into a curved slice dipped with fig
chutney.
The flavor, however, is honest: strong, smooth and sublime.
And you don’t actually need the toast for crunchiness.
This is the season for high teas, with dainty cups of fine china
and little pastries that eal to both visual and physical etites.
But there is one high tea with a difference, and Pauline D.
Loh finds out just e_actly why it is special.
Earl Grey tea and macarons are all very well for the crucial
recuperative break in-between intensive bouts of holiday season shopping.
And for those who prefer savory to sweet, there is still the
selection of classic Chinese snacks called dim sum to satisfy and
satiate.
High tea is a meal to eat with eye and mouth, an in-between
indulgence that should be light enough not to spoil dinner, but
sufficiently robust to take the edge off the hunger that strikes hours
after lunch.
The afternoon tea special at Shang-_i at the Four Seasons Hotel
Pudong has just the right elements.
It is a pering meal, with touches of lu_ury that make the high tea
session a treat in itself.
Whole baby abalones are braised and then ped on a shortcrust pastry
shell, a sort of Chinese version of the Western vol-au-vent, but
classier.
Even classier is the dim sum staple shrimp dumpling or hargow,
upgraded with the addition of slivers of midnight dark truffles.
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This is a master touch, and chef Simon Choi, who presides
unchallenged at Shang-_i, has scored a ner again.
Sweet prawns and aromatic truffles — what’s not to love? His
masterful craftsmanship is e_hibited in yet another pastry — a sweet
pastry that is shaped to look like a walnut, but which you can put
straight into the mouth.
It crumbles immediately, and the slightly sweet, nutty morsel is so
easy to eat you’ll probably reach straight for another.
My favorite is the dessert that goes by the name yangzhi ganlu, or
ambrosia from the gods.
The hotel calls it chilled mango cream with sago, pomelo and
bird’s nest – made with ingredients that resonate with every female
soul.
It does taste like ambrosia, with the sweet-sour fragrance of the
mango forming the first layer of taste and sensation, and the pomelo
sacs and sago pearls providing the tactile contrast.
The bird’s nest — it’s the ingredient that gilds the lily, since
it is supposed to nourish and nurture a perfect ple_ion.
For those unfamiliar with this e_otic ingredient, the bird’s nest
is not a bundle of twigs, but is, instead, the dried secretion that cave
swifts use to build their nest.
Technically, it’s bird saliva, but the Chinese believe that it has
collagen-boosting properties essential to beauty.
To me, it just tastes good, adding a slight gelatinous crunch to
the back of the teeth.
There is also a baked mushroom puff pastry that includes the highly
prized Matsutake or pine mushroom.