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These are questions asked by fociboy

Let's consider the function f(x)= tan(x)- x and its root in the interval (Pi/2,3*Pi/2)

Firstly, we zoom the intersection point of the function with g(x)= tan(x) and h(x)= x ( or the function f(x) and the Ox axis):

plot([tan(x),x], x= 4.3..4.55, gridlines=true);

 Now, we use the Newton-Raphson method to reach the root, like this:

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