Multivariable limit of (x,y)->(1,0) of ln(1+y^2/x^2+xy))

[jumboopizza]

multivariable limit of (x,y)--->(1,0) of ln(1+y^2/x^2+xy))

Homework Statement

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.

Homework Equations

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?

 

[STEMucator]

Your limit is extremely easy to calculate here. You can simply plug it right in. So yes the limit is actually 0, because ln(1) = 0.