Limit of Multivariable Function: ln((1+y^2)/(x^2+xy))

[munkhuu1]

Homework Statement

lim(x,y)-(1,0) ln((1+y^2)/(x^2+xy))

Homework Equations

The Attempt at a Solution

if i just substitude x and y i get ln (1)= 0 so is the limit 0?

 

[tiny-tim]

hi munkhuu1!

if i just substitude x and y i get ln (1)= 0 so is the limit 0?

almost

the limit of a product (or quotient) is the product (or quotient) of the limits if they exist,

so you also need to point out that the two limits exist

 

[munkhuu1]

hi munkhuu1!


almost

the limit of a product (or quotient) is the product (or quotient) of the limits if they exist,

so you also need to point out that the two limits exist

thank you, and so do i need to see if df/dx and df/dy exists? or something else?

 

[tiny-tim]

(in some cases, that might not be enough!)

no, just point out that it's obvious that the limits of 1 +y² and of x² + xy exist

 

[munkhuu1]

thank you.