Limit of a Two-Dimensional Function with Positive Inputs: Solving for -1/5

  • Thread starter Thread starter tt2348
  • Start date Start date
  • Tags Tags
    Dimension Limit
tt2348
Messages
141
Reaction score
0

Homework Statement


<br /> \lim _{ (x,y)\rightarrow (0^{ + },0^{ + }) }{ \frac { { e }^{ \sqrt { x+y } } }{ 4x+2y-5 } }

Homework Equations


eh.

SO I did the problem. I usually sub 1/n for 0+ in most of these, but clearly the top goes to 1 from +inf, and the bottom goes to -5... Hence... -1/5

But.
The multiple choice was

A)\stackrel{\nearrow}{\rightarrow}\frac {1 }{ 5 }

B) \frac {1 }{ 5 }


C)\stackrel{\nearrow}{\rightarrow}1

D) 1

What on Earth does \stackrel{\nearrow}{\rightarrow} mean?!??
 
Physics news on Phys.org
Nothing wrong with what you did. I have no idea what they are trying to say.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Back
Top