How do I find the intersection point of a trigonometric function and an exponential function?
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sin((π / 2) * x) + 1 = 4 – 2^(-x + 2)
sin((π / 2) * x) = 3 – (4 / 2^x)
sin((π / 2) * x) + (4 / 2^x) = 3
Now there are 2 options:
1) See and recognize sharpness since sin(π / 2) = 1 and 4 / 2^1 = 2, must be x = 1.
or
2) Use an approximation method (e.g. the Newton method).
The solution for x=1 read; that there are no further solutions, one recognizes the monotony behavior of the function g and the limitation of the function f.
PS: The two functions f and g were chosen so that they can be read their point of intersection. In general, this is not the case. Since a transcendent equation is obtained during rectification, it is generally necessary to use a numerical approximation method for the solution…