x趋向于0时, cosx的极限为什么趋向于1?

2025-03-16 10:07:17
推荐回答(5个)
回答1:

x趋向于0时,cosx的左右极限均为1。按照你的想法的话,cos π/2=0,在以x为横坐标y为纵坐标的x-y坐标系的y=cosx图像,此时x=π/2,y=0,而x=0时y=1,你把因变量和自变量搞混了。相当于你用一个y-x坐标系按照字母去对应一个x-y坐标系,自变量和因变量对应的字母已经改变了,再按照字母去对应是错误的。

回答2:

你的两个X表示的都不是一个东西 也能通用的吗? 你的第一个X是 X=cos90度,而你cosx你的x表示的是一个角度,x趋向于0 就是 相当于cos0,所以cos90度和cos0度有什么关系?你90度余弦等于0和我0度余弦等于1有什么冲突,而且cos和sin都是连续函数,它们在点的极限值是等于点的函数值的。总之,你的两个x代表的就不是一个东西。

回答3:

sin90度里的90度相当于pi/2 不是x轴上的0 cos90度的y值是0,对应的x轴的坐标是pi/2

回答4:

当x趋向于0时,cosx趋向于1,但此时始终小于1,cosx-1<0,故取根号无意义。

回答5:

搞笑,为什麼趋向0和趋向无穷会一样?你这个结论从哪里来?
y=cosx是在R上的连续函数,所以求极限直接把x=0代入就得y=cos0=1

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