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若A={2,3,4},B={x|x=n×m,m,n∈A,m≠n},则集合B的元素...
若A={2,3,4},B={x|x=n×m,m,n∈A,m≠n},则集合B的元素个数为 .
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提高过江大桥的车辆通行能力可改善整个城市的交通状况,在一般情况下,大桥上的车流速度v(单位:千米/小时)是车流密度x(单位:辆/千米)的函数,当桥上的车流密度达到200辆/千米时,造成堵塞,此时车流速度为0;当车流密度不超过20辆/千米时,车流速度为60千米/小时,研究表明:当20≤x≤200时,车流速度v是车流密度x的一次函数.
(I)当0≤x≤200时,求函数v(x)的表达式;
(Ⅱ)当车流密度x为多大时,车流量(单位时间内通过桥上某观测点的车辆数,单位:辆/小时)f(x)=x•v(x)可以达到最大,并求出最大值.(精确到1辆/小时).
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已知函数f(x)=
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+
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,曲线y=f(x)在点(1,f(1))处的切线方程为x+2y-3=0.
(Ⅰ)求a、b的值;
(Ⅱ)证明:当x>0,且x≠1时,f(x)>
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.
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在△ABC中,内角A,B,C的对边分别为a,b,c.已知cosA=
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,sinB=
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C.
(1)求tanC的值;
(2)若a=
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,求△ABC的面积.
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设函数f(x)=
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cos(2x+
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)+sin
2x
(Ⅰ)求f(x)的最小正周期;
(Ⅱ)设函数g(x)对任意x∈R,有g(x+
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)=g(x),且当x∈[0,
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]时,g(x)=
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-f(x),求g(x)在区间[-π,0]上的解析式.
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已知向量
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=(sinx,1),
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=(
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Acosx,
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cos2x)(A>0),函数f(x)=
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•
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的最大值为6.
(Ⅰ)求A;
(Ⅱ)将函数y=f(x)的图象像左平移
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个单位,再将所得图象各点的横坐标缩短为原来的
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倍,纵坐标不变,得到函数y=g(x)的图象.求g(x)在[0,
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]上的值域.
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