Prove that there exists only one number

Hanzikoval1pa

Hanzikoval1pa

Answered question

2022-03-31

Prove that there exists only one number xR such that sin(x)=x1

Answer & Explanation

mhapo933its

mhapo933its

Beginner2022-04-01Added 9 answers

Let
f(x)=sinxx+1
Note that
f(0)=1>0
and
f(π)=π+1<0
It is implied by the intermediate value theory that there is some x(0,π) for which f(x)=0
Note that
f(x)=cos(x)10
It means that there are no turning points and your function isn't expanding.
The answer is special as a result.

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