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5x+cosx=0show that the equation 5x+cosx=0 has a solution.Are there many solution?
题目详情
5x+cosx=0
show that the equation 5x+cosx=0 has a solution.Are there many solution?
show that the equation 5x+cosx=0 has a solution.Are there many solution?
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答案和解析
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
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
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