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函数极限的应用题一个温度计离x厘米远的蜡烛火焰,设f(x)为为摄氏度的度数在温度计上,假设温度计的玻璃会爆炸如果接触了火

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函数极限的应用题
一个温度计离x厘米远的蜡烛火焰,设f(x)为为摄氏度的度数在温度计上,假设温度计的玻璃会爆炸如果接触了火焰,
(a)从物理的角度上解释f(0)不存在?
(b)根据温度计的尺度,描述lim x趋进o f(x)的意义?
(c)如何温度计的最大尺度为200 C,蜡烛火焰的最高温度为400 C.画一个现实的图像f(x)?
原文是
A thermometer is stationed at x centimeters from a candle flame.Let f(x) be the Celsius scale reading on the thermometer.Assume that the galss in the thermometer will crack upon contact with the flame.
a.Explain physically why f(0) does not make any sense.
b.Describe in terms of the thermometer scale the meaning of lim x趋进0 f(x) (i.e the limit of f(x) as x approaches zero through positive values)
c.Draw a realistic graph of f(x) for a scale with maximum balue 200'C (Assume that the flame temperature is 400'C)
a)
因为温度计不可能和蜡烛火焰放在同一点,否则会发生爆炸
because x=0 means that we put the thermometer at the point of the candle frame,which will cause the thermometer crack.
b)
意义是我们可以从趋进的方向,也就是通过极限得到火焰的温度
its purpose is to get the centigrade of the flame through getting the limit of f(x) as x->0
c)
(我就不画了,应该是个递减函数,x=0的时候显然应该是400,所以x的范围,最小也就是〔f(200)〕^(-1),此处说-1的是逆函数,而且x应该没有最大值,向x趋向于无穷的地方,应该是f(x)->0,not f(x)=0)