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问题 填空题
设曲线y=（ax-1）ex在点A（x0，y1）处的切线为l1，曲线y=（1-x）e-x在点B（x0，y2）处的切线为l2．若存在x0∈[0，
3
2
]，使得l1⊥l2，则实数a的取值范围为______．
答案

函数y=（ax-1）ex的导数为y′=（ax+a-1）ex，

∴l1的斜率为k1=(ax0+a-1)ex0，

函数y=（1-x）e-x的导数为y′=（x-2）e-x

∴l2的斜率为k2=(x0-2)e-x0，

由题设有k1•k2=-1从而有(ax0+a-1)ex0•(x0-2)e-x0=-1

∴a（x02-x0-2）=x0-3

∵x0∈[0，

3
2
]得到x02-x0-2≠0，所以a=
x0-3
x20
-x0-2
，

又a′=

-(x0-1)(x0-5)
(
x02
-x0-2)2
，另导数大于0得1＜x0＜5，

故

x0-3
x20
-x0-2
在（0，1）是减函数，在（1，
3
2
）上是增函数，

x0=0时取得最大值为

0-3
02-0-2
=
3
2
；

x0=1时取得最小值为1．

∴1≤a≤

3
2

故答案为：1≤a≤

3
2

单项选择题

柏油便见于（）。

A．痔疮

B．消化道出血

C．阻塞性黄疸

D．阿米巴痢疾

E．过敏性肠炎
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单项选择题

Even plants can run a fever, especially when they are under attack by insects or disease. But (1) humans, plants can have their temperature (2) from 3,000 feet away—straight up. A decade ago, (3) the infrared scanning technology developed for military purpose and other satellites, physicist Stephen Paley (4) a quick way to take the temperature of crops to determine (5) ones are under stress. The goal was to let farmer (6) target pesticide spraying (7) rain poison on a whole field, which (8) include plants that don’t have the pest problem.

Even better, Paley’s Remote Scanning Services Company could detect crop problem before they became (9) to the eye. Mounted on a plane flown at 3,000 feet (10) , an infrared scanner measured the heat emitted by crops. The data were (11) into a color-coded map showing (12) plants were running "fevers". Farmers could then spot spray, using 50 to 70 percent less pesticide than they (13) would.

The bad news is that Paley’s company closed down in 1984, after only three years. Farmers (14) the new technology and long-term backers were hard (15) . But with the renewed concern about pesticides on produce, and refinements in infrared scanning, Paley hopes to (16) into operation. Agriculture experts have no doubt about the technology works. "This technique can be used (17) 75 percent of agricultural land in the United States," says George Oerther of Texas A＆M. Ray Jackson, who recently retired from the Department of Agriculture, thinks (18) infrared crop scanning could be adopted by the end of the decade. But (19) Paley finds the financial backing (20) he failed to obtain 10 years ago.

17（）

A.of

B.in

C.for

D.on
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