multivariable limit of (x,y)--->(1,0) of ln(1+y^2/x^2+xy)) 1. The problem statement, all variables and given/known data limit of (x,y)--->(1,0) of ln(1+y^2/x^2+xy)) Find the limit, if it exists, or show that the limit does not exist. 2. Relevant equations 3. The attempt at a solution so i have: lim(x,y)---->(1,0) ln(1+y^2/x^2+xy) i rewrote it as: ln(1+y^2)-ln(x(x+y)) holding the y constant at 0 i get=lim x-->1 0-ln(x^2)=0 holding x constant at 1 i get=lim y---> ln(1)-(ln(1)=0 but my question is,is the limit actually 0? or would i have to approach (1,0) from somwhere else? i tried to approach (1,0) from a line (x=1+y) only to end up even more confused lim(1+y,y) ln(1+y^2)-ln(1+y(1+2y))=0? so does the limit actually = 0? or am i making a mistake somewhere?