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蚂蚁如何逃跑

蚂蚁如何逃跑. 一块长方形的金属板，四个顶点的坐标分 别是(1,1), (5,1), (1,3)和(5,3). 在坐标原点 处有一个火焰，它使金属板受热. 假定板上 任意一点处的温度与该点到原点的距离成 反比. 在(3,2)处有一只蚂蚁，问这只蚂蚁 应沿什么方向爬行才能最快到达较凉快的 地点？. 蚂蚁如何逃跑. 解： 板上任一点 ( x,y) 处的温度. k 是一个比例常数. 温度变化最骤烈的方向是梯度所指方向. 计算. 蚂蚁如何逃跑. 它的单位矢量.

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蚂蚁如何逃跑

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  1. 蚂蚁如何逃跑 一块长方形的金属板，四个顶点的坐标分别是(1,1), (5,1), (1,3)和(5,3). 在坐标原点处有一个火焰，它使金属板受热. 假定板上任意一点处的温度与该点到原点的距离成反比. 在(3,2)处有一只蚂蚁，问这只蚂蚁应沿什么方向爬行才能最快到达较凉快的地点？

  2. 蚂蚁如何逃跑 解：板上任一点(x,y)处的温度 k 是一个比例常数. 温度变化最骤烈的方向是梯度所指方向. 计算

  3. 蚂蚁如何逃跑 它的单位矢量 所指的方向是由热变冷变化最骤烈的方向（其反方向则是由冷变热）. 蚂蚁虽然不懂梯度，但凭它的感觉细胞的反馈信号，它将沿这个方向逃跑.

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