Showing surjectivity of f(x) = \frac{x - \sin x}{1 - \cos x} is strictly monotonically inc

Deven Livingston

Deven Livingston

Answered question

2022-05-02

Showing surjectivity of f(x)=xsinx1cosx
is strictly monotonically increasing on x(0,2π) , I'd like to show the surjectivity of this function [to (0,)]. However, I fail solving the equation
y=xsin(x)1cos(x)
with respect to x. Can I somehow use/apply the fact that f(x)=u(x)u(x)?

Answer & Explanation

Leia Wiggins

Leia Wiggins

Beginner2022-05-03Added 18 answers

Just show that the function is continuous in the domain, and since it tends to 0 as x0 , and tends to as x2π , you are done as you have already shown it's monotonically increasing in the domain.

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