if I am trying to find the limit of e^(-xy)cos(x+y) as (x,y)-(1,-1) what would be good numbers to try

Question

if I am trying to find the limit of e^(-xy)cos(x+y) as (x,y)->(1,-1) what would be good numbers to try

anonymous · Answer

Hi d4millers,

The exponential and trigonometric functions are functions that obtain their limits (some functions don't).  Polynomials are another example of functions that obtain their limits.  So, in these cases, the limits can be found by substitution of the limit-point.  Here, sub. (1,-1) into your equation to get,$$\lim_{(x,y) \rightarrow(1,-1)}e^{-xy}\cos(x+y)=e^{-(1)(-1)}\cos((1)+(-1))$$$$=e^1{\cos(0)}=e$$

anonymous · Answer

I'm sorry Lokisan, for mis info. I am trying to see if the limit exists. So In essence I am checking different paths but am getting confused in which way to go. if that makes sense.