Let $f(x) = \arctan x + \mathop{\text{arccot}} x$. find $f(0) + f(1) + f(\sqrt{2}) + f(\sqrt{3})$.

By direct computation, arctan(0) = 0, arccot(0) = pi/2, arctan(1) = arccot(1) = pi/4.

Let a = arctan(sqrt(2)). Then cot(3*pi/2 - a) = cot(pi/2 - a) = tan(a) = sqrt(2), so arccot(sqrt(2)) = 3*pi/2 - a. Therefore, arctan(sqrt(2)) + arccot(sqrt(2)) = 3*pi/2.

Similarly, arctan(sqrt(3)) + arccot(sqrt(3)) = 3*pi/2.

So the answer is 0 + pi/2 + pi/4 + pi/4 + 3*pi/2 + 3*pi/2 = 4*pi.

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step-by-step explanation:

; oqirjg'

in mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. there are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. the set of candidate solutions that satisfy all constraints is called the feasible set.

hoped i'm right lol