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

In summary, a two dimension limit refers to understanding the behavior of a function in a two-dimensional space as it approaches a specific point. It can be calculated using similar principles as a one-dimensional limit, but multiple approaches may need to be considered. This concept is significant in mathematics as it allows for the analysis of functions in a two-dimensional space, with applications in calculus, geometry, and physics. Some common examples of two dimension limits include finding the limit of a function on a graph, determining the slope of a curve, and calculating area under a curve using Riemann sums. In the real world, two dimension limits are used for predicting object behavior, analyzing population growth, and maximizing profits in business, as well as in engineering, economics,
  • #1
tt2348
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Homework Statement


[itex]
\lim _{ (x,y)\rightarrow (0^{ + },0^{ + }) }{ \frac { { e }^{ \sqrt { x+y } } }{ 4x+2y-5 } } [/itex]

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)[itex]\stackrel{\nearrow}{\rightarrow}\frac {1 }{ 5 } [/itex]

B) [itex]\frac {1 }{ 5 } [/itex]


C)[itex]\stackrel{\nearrow}{\rightarrow}1[/itex]

D) 1

What on Earth does [itex]\stackrel{\nearrow}{\rightarrow}[/itex] mean?!??
 
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  • #2
Nothing wrong with what you did. I have no idea what they are trying to say.
 

1. What is a two dimension limit?

A two dimension limit refers to the concept of a mathematical limit in a two-dimensional space. It involves understanding how a function behaves as it approaches a specific point in a two-dimensional coordinate system.

2. How is a two dimension limit calculated?

A two dimension limit can be calculated using the same principles as a one-dimensional limit. The main difference is that in a two-dimensional space, the function approaches the point from any direction, so multiple approaches may need to be considered to determine the limit.

3. What is the significance of a two dimension limit in mathematics?

A two dimension limit is important in mathematics because it allows us to analyze the behavior of functions in a two-dimensional space. This is useful in many areas such as calculus, geometry, and physics.

4. What are some common examples of two dimension limits?

Some common examples of two dimension limits include finding the limit of a function as it approaches a specific point on a graph, determining the slope of a curve at a specific point, and calculating the area under a curve using Riemann sums.

5. What are some real-world applications of two dimension limits?

Two dimension limits have many real-world applications, such as predicting the behavior of a moving object, analyzing the growth rate of a population, and determining the maximum profit for a business. They are also essential in fields such as engineering, economics, and computer science.

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