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

  • #1
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?
 

Answers and Replies

  • #2
STEMucator
Homework Helper
2,075
140


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.
 

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