问题 填空题
给出下列命题:①y=lg(sinx+
1+sin2x
)
是奇函数;
②若α,β是第一象限角,且α>β,则cosα<cosβ;
③函数f(x)=2x-x2在R上有3个零点;
④函数y=sin2x的图象向左平移
π
4
个单位,得到函数y=sin(2x+
π
4
)
的图象.
其中正确命题的序号是______.(把正确命题的序号都填上)
答案

函数f(x)=lg(sinx+

1+sin2x
)的定义域为R,

且f(-x)+f(x)=lg(sin(-x)+

1+sin2(-x)
)+lg(sinx+
1+sin2x
)
=lg1=0,

即f(-x)=-f(x)

∴①y=lg(sinx+

1+sin2x
)是奇函数正确;

若α,β是第一象限角,且α>β,但α,β不一定在同一单调区间上,则cosα<cosβ不一定成立,故②错误;

在同一平面坐标系中画出y=2x与函数y=x2的图象,易得两函数的图象共有3个交点,故③函数f(x)=2x-x2在R上有3个零点正确;

函数y=sin2x的图象向左平移

π
4
个单位,得到函数y=sin[2(x+
π
4
)]
=sin(2x+
π
2
)
的图象,故④错误.

故答案为:①③

单项选择题

"What does the middleman do but add to the price of goods in the shops " Such remarks are aimed at the intermediate operations between manufacturers and final customers. This practice usually attracts a lot of attention from the public and the press and the operation most talked about is what is often called wholesaling.
The wholesaler buys goods in large quantities from the manufacturers and sells them in smaller parcels to retailers, and for this service his selling price to the retailer is raised several percent higher. But his job is made more difficult by retail demand not necessarily running level with manufacturers’ production. Because he adjusts or regulates the flow of goods by holding stock Until required, he frees the manufacturer, to some extent, from the effect on production of changing demand and having to bear the whole risk.
The manufacturer can then keep up a steady production flow, and the retailer has no need to hold heavy stocks, who can call on the wholesaler for supplies any time. This wholesale function is like that of a valve in a water pipe. The middleman also bears part of the risk that would otherwise fall on the manufacturer and also the retailer.
The wholesaler provides a purely commercial service, for which he is too well rewarded. But the point that is missed by many people is that the wholesaler is not just someone adding to the cost of goods. It is true one could eliminate the wholesaler but one would still be left with his function: that of making sure that goods find their way to the people who want them.

"Middleman" in the passage almost equals to all the following in meaning EXCEPT ______.

A.go-between

B.intermediary

C.manufacturer

D.wholesaler

单项选择题