设[tex=5.143x1.286]KBMvwjT+F0heo284zNK0+Q==[/tex],试按定义求[tex=2.786x1.286]DrxaUfJM3lh/5Dz7woXCoh9zV+7ywi+a/q325PfMX6Y=[/tex]
解:【按定义求导数,对初学者可依三个步骤进行:写出增量[tex=1.357x1.286]dlo2nBSXIW5A7hLNsiI3ow==[/tex],计算比[tex=1.571x2.071]R/BgIVYP86M8AKVRsj5c4U9ju37FeinnA7aJKFfnAPI=[/tex],求出极限[tex=3.929x2.071]g+TnzZrx8UZmBWGntValuOQkLl6XQ+FjiWKa5459q2ss5chVfmclFy7QW4ne6qkqGZeW1fB3Kgx61WGofuxEhg==[/tex]】[tex=5.714x1.286]5zET9n/RJxMEroNltOnqwgy/2i8w4AEzOkYEnddBQWZo9g/cD8TvI0lDDBMhAHNs[/tex],[tex=12.143x1.286]MTcGGIPNfvQI4rryd7onM0eXYWGXLNbgkLt+HzLqjeITzC9QtD+2t5x7vhNSNklIWYeaNpnNSYuYF+pJGDVOLyj1KNPJLgs2xgd3P7EI5+U=[/tex],这里[tex=3.5x1.286]fUwp9QkJKUEZuNpb7mEONA==[/tex],[tex=0.714x1.286]Mjp1ERIg12NQkOrp1BseMg==[/tex] [tex=23.071x1.286]QMzjk60clcWZDwW8pzl/NKD5av7n7ILNeQqh581VEg8qqSMF8cknm5qxYDpyYc1eKCwfxKH79IVRGi3kVH8/nirQ3PKXEpct6q3XJgcDapwGQMa+ZnueTn+xX2Ggj+v8[/tex], [tex=13.571x2.214]R/BgIVYP86M8AKVRsj5c4Rl5r0mvlN5iF7fZcNxHW1hxd8fiZTPm/FsqX6QsQoFNbSulu8WbKLOn98QYsfFKgvo2CJFilelBokxdyzoJM8TNdSxXyD6/3z//5i0YwJZh[/tex] [tex=0.714x1.286]Mjp1ERIg12NQkOrp1BseMg==[/tex][tex=19.643x2.214]L7DxoBuKg4U3yOJWr6WxYJ/wJSzrrjTIOWvBTitWJQe/HbcZtO5xMLA2ZG5HF4gX6RaVk1blmdnuwvGuM7x2Qb3nZo5xUSzrv1aH5gde+FRqmRAu5S8KXQuPNhQNlyNgONH5XnNNDEkQMd3oHT6A8azY0FOAHVS45d9AlzXtz5Mo8HJvMNxSxKIZq+iNevzXvxD2ZP28yqed+iBlFtCzXAYfKMIZrFjBeFgvJRWP5zY=[/tex][tex=13.714x2.071]IT0AOBH9mu0QevyT7UxbItysz5/0Oa2fCLU5KBzKci3rRjPArPtogdYcwe+wDlbMgPcAK3YzziZwfroNxM2jEQlNL62tVEsIjXspIKfEhkl0rwMBpHwOaFQEUYrwk1SU[/tex]
举一反三
- 设两个消费者a和b消费两种产品x和y。消费者a的效用函数为u= u(x,y),消费者b的无差异曲线为 [tex=4.071x1.214]rMu/HIPxF2QZiXIQBxo5CQ==[/tex]([tex=0.929x1.0]y9I2+d6xhn1Hp5ai8uEm/Q==[/tex]>0,k>0)。试说明交换的契约曲线的倾斜方向。
- 设随机变量(X,Y)的概率分布列为[img=345x154]178ab1c9ce3bc1b.png[/img]求[tex=1.571x1.0]JUrGU6ftUjxQCIr6CyfDwQ==[/tex],[tex=1.357x1.0]yL/7/hhyqgwzAX8jnIq3OQ==[/tex],[tex=4.357x1.357]LN0xwhQHSOeLwBClUlpHQw==[/tex].
- 设f(x)具有性质:[tex=8.571x1.357]8gPeznjMnng12qtkk9Vgczii1Sh4d1qJxc9iHYT5+YI=[/tex]证明:必有f(0)=0,[tex=5.5x1.357]rt5qCY7TXHcsFUQrD44nPA==[/tex](p为任意正整数)
- 设X,Y为两个随机变量,且P{X ³0,Y ³ 0} = 3/7 , P{X ³ 0} = P{ Y ³ 0} = 4/7 ,则P{max(X, Y) ³ 0} = ( ). A: 1/7 B: 3/7 C: 4/7 D: 5/7
- 设抛物线[tex=7.5x1.429]PuOOiuXliw3SbXOlC3PxEg==[/tex]与x轴有两个交点x=a,x=b(a<b).函数f在[a,b]上二阶可导,f(a)=f(b)=0,并且曲线y=f(x)与[tex=7.5x1.429]PuOOiuXliw3SbXOlC3PxEg==[/tex]在(a,b)内有一个交点.证明:存在[tex=3.286x1.357]EV4pc+LBkNBOhd4NZUA5NQ==[/tex],使得[tex=4.357x1.429]/FYTUVhgTPYa3RqQR+bSSXpHSralD3pTYi2H35Z8qsw=[/tex].
内容
- 0
设函数f(x)在[tex=3.286x1.357]64m0xE4nFlaKGIakApV0PA==[/tex]上连续,且有f(0)=0及f'(x)单调增,证明:在[tex=3.5x1.357]vgrW1/jK/GZ1TOWaPFIQWA==[/tex]上函数[tex=5.071x2.429]KmCvFjqAEA9O51+9erVGP+KtDDqVtXZQWqxj1eiTO5k=[/tex]是单调增的。
- 1
设随机变量X与Y,且D(X)=25 . D(Y)=36 .[tex=6.929x1.357]YRHgHmN/yZW92ECOHesamh6DUEs33HnR+2dxr68Tcr4=[/tex]求[tex=4.286x1.357]wxsI0NJpCsUWd6vdcOiJiw==[/tex]
- 2
设[tex=8.429x1.357]nrpdm/CWmnzWBrNVydZQ4OwFYiTQ3q0L6zS4h3ythMgdg0CLDO+FStyCKlQj3C8a[/tex],求x和y
- 3
求[tex=1.571x1.5]InBONLymcD+/JHFX8MFz/Q==[/tex],设[tex=4.286x1.214]/bMzoNPkMGqIXVfV4w5BWsGCSFhgKVrvOohFltlKb9g=[/tex]
- 4
设f(x)在[0,a]上连续,在(0,a)内可导,且f(a)=0,证明至少存在一点[tex=3.643x1.357]lTsOOhJ85nTn3mrT2Mx0lw==[/tex]使[tex=6.286x1.429]JZ8spbP5y8lrG0FgeChLIS7LPAFOZNl0MwLjGUb1ZoE=[/tex]