The function F(x,y) = arctan(x + √y is continuous at points where the expression inside the arctan is defined. Specifically, the square root function √y requires y to be non-negative (y ≥ 0). Thus, the set of points at which F is continuous is defined by the condition that y must be greater than or equal to zero, allowing for all real values of x. The discussion highlights the importance of understanding the domain of the function and the implications of continuity in multivariable calculus.
PREREQUISITESStudents studying calculus, particularly those focusing on multivariable functions, as well as educators looking for examples of continuity in mathematical analysis.
SneakyG said:Homework Statement
Determine the set of points at which the function is continuous.
F(x,y) = arctan(x + √y)
Homework Equations
Perhaps the chain rule?
The Attempt at a Solution
I derived it, but the solution in the back of the book is nothing like what I expected. It involves e and other trig functions.