Tough multivariable limit

  • #1

Homework Statement



Evaluate this limit,

lim (x,y) > (0,0) f(x,y)

where f(x,y) = ((8x+8)(2x+3y)^2) / (sqrt(3x^2 + 14xy + y^2) - sqrt(x^2 -2xy + 8y^2))

Homework Equations



No?

The Attempt at a Solution



I figure the first attempt is to rationalize this fraction. But after I rationalized it, it came out as

f(x,y) = (sqrt(3x^2 + 14xy + y^2) + sqrt(x^2 -2xy + 8y^2)(8x+8)(2x+3y)^2) / (2x^2 + 16xy - 7y^2)

Which to me is way to complicate it, I tried to approach from (x > y) , (y > x) , (x > 0) , (y > 0) but it does not get simplified at all.
 

Answers and Replies

  • #2
jbunniii
Science Advisor
Homework Helper
Insights Author
Gold Member
3,472
251
OK, so try working with this part:

(8x+8)(2x+3y)^2) / (2x^2 + 16xy - 7y^2)

Multiply out the numerator so you get one polynomial divided by another, then carry out the division and see what you get.
 

Related Threads on Tough multivariable limit

  • Last Post
Replies
10
Views
1K
  • Last Post
Replies
1
Views
996
  • Last Post
Replies
1
Views
994
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
3
Views
896
  • Last Post
Replies
3
Views
957
  • Last Post
Replies
10
Views
803
  • Last Post
Replies
13
Views
1K
  • Last Post
Replies
3
Views
992
Top