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微积分题目

解:1。∵dy/dx=(xy²-cosxsinx)/(y(1-x²)) ==>y(1-x²)dy=(xy²-cosxsinx)dx ==>y(1-x²)dy-xy²dx+cosxsinxdx=0 ==>(1-x²)d(y²)-y²d(x²)+sin(2x)dx=0 ==>2(1-x²)d(y²)+2y²d(1-x&#...

解:1。∵dy/dx=(xy2-cosxsinx)/(y(1-x2)) ==>y(1-x2)dy=(xy2-cosxsinx)dx ==>y(1-x2)dy-xy2dx+cosxsinxdx=0 ==>(1-x2)d(y2)-y2d(x2)+sin(2x)dx=0 ==>2(1-x2)d(y2)+2y2d(1-x2)+sin(2x)d(2x)=0 ==>2d(y2(1-x2))+sin(2x)d(2x)=0 ==>2y2(1-x2)-cos(2...

积分变量是x,与z无关,所以1-e^(-z)提出去了,然后e^(-x)的积分是-e^(-x)

1.选择D; 2.最高次数为1+2=3次。 3.即是3次无穷校

解:1。∵dy/dx=(xy²-cosxsinx)/(y(1-x²)) ==>y(1-x²)dy=(xy²-cosxsinx)dx ==>y(1-x²)dy-xy²dx+cosxsinxdx=0 ==>(1-x²)d(y²)-y²d(x²)+sin(2x)dx=0 ==>2(1-x²)d(y²)+2y²...

应该是这样 看一下

解:1。∵dy/dx=(xy²-cosxsinx)/(y(1-x²)) ==>y(1-x²)dy=(xy²-cosxsinx)dx ==>y(1-x²)dy-xy²dx+cosxsinxdx=0 ==>(1-x²)d(y²)-y²d(x²)+sin(2x)dx=0 ==>2(1-x²)d(y²)+2y²...

可用初等数学解决:e^x>0且x^(-ⅹ)>0,故依均值不等式得y=2e^x+e^(x) ≥2√[2e^x·e^(-x)] =2√2,故2e^x=e-x,e^x=√2/2时,所求极小值为ymin=2√2。用微分法,则如下图所示:

1.微分在近似计算中的应用: 要在半径r=1cm的铁球表面上镀一层厚度为0.01cm的铜,求所需铜的重量W(铜的密度k=8.9g/cm^3)(说明:cm^3后面的3是幂,也就是立方厘米,下面的r^3也是指r的3次方,依此类推) 解:先求镀层的体积,再乘以密度,便得...

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