Epsilon-Delta for Multivariable functions
Ok, epsilon-delta was the only thing that gave me trouble in calculus in high school and now in Calc III in college, it has only gotten worse.
I have looked at the other examples on here for multivariable limit proofs, and most of them either are slightly trivial because the point the limit is being evaluated at is (0,0), or I am unable to follow the logic. It seems like, many times, people just pull a value for delta, based on epsilon, out of thin air.
My problem is:
lim (x,y) -> (5,2) of 4xy = 40
I have the implication set up, 0< [(x-5)^2 + (y-2)^2]^(1/2) < delta
|(4xy)-40| < epsilon
but I don't know how to manipulate that properly.
It's particularly frustrating because this topic isn't even in our textbook- our professor just foisted it on us with little to no preface.