# How do I find the limit to an intersection of two functions?

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Pedro Almeida il 29 Nov 2022
Commentato: Bjorn Gustavsson il 29 Nov 2022
I have this exercise to find the limit to an intersection of two functions I have no idea how to do it, some gidance would be helpful
Two material points move towards each other through two laws of motion given by y1(t) = a − sin(t), y2(t) = t, 'a' being a real parameter. We designate by τa ∈ R the instant when the two trajectories intersect. Determine an interval Ia = [b1, b2], 0 < b1 < b2, of admissible values for the parameter a, in order to guarantee that τa ∈ I = [1, 2].
I'm told I have to use Bolzano's Theorem, but still I don't know how to apply it.
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Torsten il 29 Nov 2022
Hint: Consider
1 + sin(1)
ans = 1.8415
2 + sin(2)
ans = 2.9093
Bjorn Gustavsson il 29 Nov 2022
Just plot the two functions for a couple of parameter-combinations. This will give you some visual/physical insight in what the functions actually mean. Then have a think.

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