The function f(x)=arctan(2x/x^2-1). Is known that the exist constant A,C1, C2, C3 such that

Question

The function f(x)=arctan(2x/x^2-1). Is known that the exist constant A,C1, C2, C3 such that

f(x)={A arctan(x) + C1, if x < -1,

A arctan(x) +C2, if -1< x <1,

A arctan(x) +C3, if x >1}

Find the constants A,C1,C2, and C3.

Answer 1

Graphing the function, you will see that there are asymptotes at x = -1.0 and 1.0

So as x approaches -1.0 from the left, y approaches -89.999...

and as x approaches -1.0 from the right, y approaches 90.0001...

and as x approaches 1.0 from the left , y approaches -89.999...

and as x approaches 1.0 from the right, y approaches 90.0001....

so then A, C1, C2, C3 are the values respectively of y above.for the 4 cases