1. The problem statement, all variables and given/known data lim (x,y)->(0,0) (cos(x) - 1 + (x^2/2)) / ( x^4 + y^4) 3. The attempt at a solution Am I correct in assuming that I have to solve by looking for a path where the limit doesn't exist/is different to another path (given that the epsilon thing is beyond the scope of the course)? I've tried finding it along the path y=0, x=0 and y=kx, and every time I've found it approaches infinity. Not sure if I've done anything wrong or not, but looking at a graph of the function, it looks like approaches along the y=0 and x=0 lines should give me different limits (according to the answer, the limit does not exist at 0,0). Any help? 1. The problem statement, all variables and given/known data OK, I'm fairly sure I've gotten the above question right, but am stuck on another. Find the limit of the following function using the Sandwich Theorem: f(x,y) = (7x^2y^2)/(x^2 + 2y^4) as (x,y)->(0,0) How would we go about it? Seeing as all terms are non-negative, zero will always be =<, but how about finding an function that's >= and also simpler to solve? You couldn't multiple/divide it by a function of x and/or y, because it'd make it larger or smaller depending on if x and/or y were smaller or greater than zero, correct? And adding a function of x and/or y wouldn't make it any easier to solve... Would it be possible to just add a negative scalar (e.g. -1) to the denominator, then substitute (x,y)=(0,0) to evaluate the limit? That way, you'd have a non-zero denominator and as both numerator and denominator are continuous, it'd be very simple to solve. 0 =< f(x,y) =< (7x^2y^2)/(x^2 + 2y^4 - 1) lim 0 =< lim f(x,y) =< lim (7x^2y^2)/(x^2 + 2y^4 - 1) Therefore, lim f(x,y) = 0. Seems too simple, though. Am I missing something or is it a legitimate approach?