Thursday

October 30, 2014

October 30, 2014

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

(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 2:59amYou 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 3:29amalright 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 3:42amor 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 12:37pmthen what can i approach by as well cause i also tried y=x-1 and that was just a mess.

**Answer this Question**

**Related Questions**

calc - need to find: lim as x -> 0 of 4(e^2x - 1) / (e^x -1) Try splitting ...

Check my CALCULUS work, please! :) - Question 1. lim h->0(sqrt 49+h-7)/h = ...

Calculus - Find the limit. lim 5-x/(x^2-25) x-->5 Here is the work I have so ...

Calculus. Limits. Check my answers, please! :) - 4. lim (tanx)= x->pi/3 -(...

Calculus - lim (x^3-1)/(x^3+2x^2y+xy^2-x^2-2xy-y^2) (x,y)->(1,0) alright i ...

Calculus - Find the indicated limits. If the limit does not exist, so state, or ...

Calculus - Find the indicated limits. If the limit does not exist, so state, or ...

Calculus - Find the following limits algebraically or explain why they don’t ...

calculus again - Suppose lim x->0 {g(x)-g(0)} / x = 1. It follows necesarily ...

Calculus - Show that limit as n approaches infinity of (1+x/n)^n=e^x for any x&...