Post #636173

In Multivariable Calculus, we're going to talk about limits, continuity, and differentiability of functions of two variables. I just printed these three examples of functions that do not have a limit at the origin. Their equations are: f₁(x, y) = ((x² – y²)/(x² + y²))² f₂(x, y) = x²/(x² + y⁴) f₃(x, y) = xy/(x² + y²) Also, if we define f₁(0, 0) = 1 and f₃(0, 0) = 0, then these two functions also have the property that both partial derivatives exist at the origin, but the function is not differentiable there. You can download the files here: https://www.thingiverse.com/thing:7314735