5x+cosx=0show that the equation 5x+cosx=0 has a solution.Are there many solution?

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5x+cosx=0show that the equation 5x+cosx=0 has a solution.Are there many solution?
5x+cosx=0
show that the equation 5x+cosx=0 has a solution.Are there many solution?

5x+cosx=0show that the equation 5x+cosx=0 has a solution.Are there many solution?
令f(x)=5x+cosx
f'(x)=5-sinx,由于·-1≤sinx≤1
所以5-sinx>0
于是f(x)为单调增函数
于是f(x)=0仅有一解
即5x+cosx=0仅有一根

相等的那一点cosx=x/(根号下x平方5x加平方);然后就是解一元二次方程了,不过由图相得x应为负值.

f(x)=5x+cosx
f'(x)=5-sinx>0
f(x)全定义域增函数,只能x轴有一个交点。
只有一个解

画y=cosx,y=-5x的图象即可得,一个根。

兄弟用数形结合法:
讲题目问题转化为求交点个数问题
即函数5x与函数-cosx交点个数,
先画出5x图像,再画出-cosx图像,这两个图像画法句简单,初中生水平
然后肉眼一看就知道solution有几个了,just only one!!!只有一个

这是超越方程,最好画图像解

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