Posted by **Bryant** on Tuesday, February 28, 2012 at 2:30am.

lim (x^3-1)/(x^3+2x^2y+xy^2-x^2-2xy-y^2)

(x,y)->(1,0)

my question is can you approach (1,0) with y=x and does that change the the limit to

lim f(x,x)

(x,x)->(1,1)

in which case i get 3/4 as the limit. and if this is not how i go about doing it can you point me in the right direction?

- calculus -
**drwls**, Tuesday, February 28, 2012 at 2:59am
You cannot approach along y = x because that relationship does not apply at (1,0).

Try approaching along y = 0

Lim (x^3-1)/(x^3+2x^2y+xy^2-x^2-2xy-y^2)

= Lim (x^3-1)/(x^3 -x^2)

x->1

= Lim 3x^2/(3x^2 -2x)

x->1

= 3

I used L'Hopital's rule.

- calculus -
**Bryant**, Tuesday, February 28, 2012 at 3:29am
alright thanks, my teacher never showed us that if you set one of the variables equal to zero you can make it a one variable function. so say i approach x=0 and find the limit of that to be infinity. does the original function f(x,y) not exist?

- calculus -
**Bryant**, Tuesday, February 28, 2012 at 3:42am
or does x=0 not work because x does not equal zero on the point (1,0). cause my teacher was fairly lazy in class and used the point (0,0) for every example.

- calculus -
**drwls**, Tuesday, February 28, 2012 at 8:44am
<<or does x=0 not work because x does not equal zero on the point (1,0)? >>

It does not work because x is not 1 at y = 0, where they want the limit evaluated.

- calculus -
**Bryant**, Tuesday, February 28, 2012 at 12:37pm
then what can i approach by as well cause i also tried y=x-1 and that was just a mess.

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