Calculus
posted by Bryant .
lim (x^31)/(x^3+2x^2y+xy^2x^22xyy^2)
(x,y)>(1,0)
alright i approached this at y=0. and got the limit as 3. where else can i approach this from to see if the limit really exist which im hoping it doesn't. i tried y=x1 and that was a mess and i also tried y=mx which did nothing.

Hmmm. . . Looks like a removable singularity to me.
x^3  1 = (x1)(x^2 + xy + y^2)
x^3+2x^2y+xy^2x^22xyy^2
= x(x+y)^2  (x+y)^2
= (x1)(x+y)^2
so, f(x,y) = (x^2+xy+y^2)/(x+y)^2 for x≠1
limit as (x,y) > (1,0) = (1)/(1)^2 = 1
Respond to this Question
Similar Questions

calculus help please
hi what is lim as x reaches one of the function x/LN(x) is it one or does the limit it not exist. hi what is limit as x reaches one of the function x/LN(x) is it one or does the limit it not exist. Have you tried graphing it? 
calculus
Find lim (with x¨‡ under it) (x^21)/x or state that the limit does not exist. I'm so lost with what to do with limits...I tried to simplify the expression to lim x+lim 1/x, but from there I'm pretty dumbfounded. If anybody … 
calculus
lim (x^31)/(x^3+2x^2y+xy^2x^22xyy^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 … 
Calculus 3
Find the limit, if it exists, or show that the limit does not exist. lim of x+y/y^2x^2 as (x,y) approaches the point (1,1). 
Calculus 3
Find the limit, if it exists, or show that the limit does not exist. lim of x+y/y^2x^2 as (x,y) approaches the point (1,1). 
calculus
1)A function g is defined for all real numbers and has the following property: g(a+b)  g(a) = 4ab+2b2 find g'(x) A)4 B)4 C)2x^2 D)4x E)does not exist not so sure where to start 2)If d/dx[f(x)] = g(x) and d/dx[g(x)] = f(3x, then d^2/dx^2 … 
Calculus. Limits. Check my answers, please! :)
4. lim (tanx)= x>pi/3 (sqrt3) 1 (sqrt3) ***1 The limit does not exist. 5. lim x= x>2 2 ***2 0 1 The limit does not exist. 6. lim [[x]]= x>9/2 (Remember that [[x]] represents the greatest integer function of x.) 4 … 
Calculus help, please!
1. Evaluate: lim x>infinity(x^47x+9)/(4+5x+x^3) 0 1/4 1 4 The limit does not exist. 2. Evaluate: lim x>infinity (2^x+x^3)/(x^2+3^x) 0 1 3/2 2/3 The limit does not exist. 3. lim x>0 (x^37x+9)/(4^x+x^3) 0 1/4 1 9 The limit … 
Calculus, please check my answers!
1. Evaluate: lim x>infinity(x^47x+9)/(4+5x+x^3) 0 1/4 1 4 ***The limit does not exist. 2. Evaluate: lim x>infinity (2^x+x^3)/(x^2+3^x) 0 1 3/2 ***2/3 The limit does not exist. 3. lim x>0 (x^37x+9)/(4^x+x^3) 0 1/4 1 ***9 … 
mathematics
Show that the limit does not exist for the function Lim (x,y)➡(1,2): (4x^3y^2  2xy^5+ 7y1)/ ( 3yy^4 + 3x^3)