- #1
mrcleanhands
So say I have an arbitrary function and I want to know it's limit as x,y approaches 0.
I could test what happens when the x-axis approaches 0, y-axis as it approaches 0 but there are some functions where I'm told that I also need to test what happens when y=mx approaches 0, and then y=x^2 and x=y^2 and I'm quite confused as to how we know what lines to approach 0 on and what functions those lines are in 3D and how ones works that out. I've basically lost any form of intuition here.
I could test what happens when the x-axis approaches 0, y-axis as it approaches 0 but there are some functions where I'm told that I also need to test what happens when y=mx approaches 0, and then y=x^2 and x=y^2 and I'm quite confused as to how we know what lines to approach 0 on and what functions those lines are in 3D and how ones works that out. I've basically lost any form of intuition here.