(adsbygoogle = window.adsbygoogle || []).push({}); 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?

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

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