问题 选择题

曲线y=ex在点(2,e2)处的切线与坐标轴所围三角形的面积为(  )

A.e2         B.2e2         C.e2         D.

答案

答案:D

欲切线与坐标轴所围成的三角形的面积,只须求出切线在坐标轴上的截距即可,故先利用导数求出在x=2处的导函数值,再结合导数的几何意义即可求出切线的斜率.最后求出切线的方程,从而问题解决.

解析:依题意得y′=ex

因此曲线y=ex在点A(2,e2)处的切线的斜率等于e2

相应的切线方程是y-e2=e2(x-2),

当x=0时,y=-e2

即y=0时,x=1,

∴切线与坐标轴所围成的三角形的面积为:

S=1/2×e2×1=

故选D.

选择题
单项选择题

American Museum of Natural History is one of the largest natural and historic museums in the world and one of the main natural history research and education centres in the United States, set up in 1869 and located in the west of the Central Park, Manhattan District, New York. It (1) 7 hectares in its total area, (2) classical types of buildings. The (3) of ancient creatures and humanity is (4) the first place of all the museums in the world, (5) the representative samples from South America, Africa, Europe, Asia and Australia were collected, besides those from the (6) country, the United States.

In the museum, there are five kinds of exhibits, including astronomy, mineralogy, human history, and animals in the (7) times and those in modern times. There are thirty-eight exhibition halls with different (8) from 500 to 1,500 square metres. Besides these, there is a Roosevelt Memorial Hall in (9) of President Roosevelt who supported the (10) of the museum, which is also used to have a special exhibition, showing the new important (11) on natural sciences and (12) affairs and social problems, and special topics connected closely with the life of the citizens. Besides this, it is also used for avocation (13) to have all kinds of scientific activities in the laboratories, centres of natural science and centres for citizens. There are more than 10 (14) research departments mainly (15) for collection of samples, research and work of publication.

In the museum, there are (16) and sub-libraries of Aulspond ancient amniote, with about 300 thousand books and magazines (17) natural history, many of (18) are very valuable monographs for the first edition. It has published many expert books and magazines, and a large number of propaganda materials, (19) which are the two magazines, Natural History and Members of Museum that have the biggest (20) of their magazines.

14()

A.subject

B.declaration

C.course

D.rehearsal