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Explain why the equation cosx=x has at least one solution. (without using a graph)
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Explain why the equation cosx=x has at least one solution. (without using a graph)
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y=cos x-x in the interval -1<=x<=1
(y(-1)=1.54>0 y(1) =-0.46 <0
y´=-sin x-1 <0 so y is decreasing from + to - so there is one and only one root in the interval