# Help limit problem multivariable

• yaho8888
In summary, the limit of (x^2+y^2)/((root(x^2+y^2+1) - 1) as (x,y) approaches (0,0) is 2. This can be found by switching to polar coordinates and using techniques such as L'Hopital's rule or rationalizing the denominator. Patience is also important when seeking help.
yaho8888

## Homework Statement

lim (x^2+y^2)/((root(x^2+y^2+1) - 1)
(x,y)-->(0,0)
what is the limit

none

## The Attempt at a Solution

$$\lim_{(x,y) \to (0,0)} \frac {x^2 + y^2}{\sqrt{x^2 + y^2 + 1} - 1} = \lim_{r \to 0} \frac {r^2}{\sqrt{r^2 + 1} - 1}$$

I got this far the answer are 2 but i don't know how it is 2.

how come no one is helping?

Perhaps because people are not sitting around with nothing to do but answer your questions! You waited a whole 29 minutes? Patience, grasshopper.

Switching to polar coordinates is a very good idea. That way, (x,y) going to (0,0) is the same as the single variable, r, going to 0. As long as the result is independent of the angle $\theta$, that is the limit. Now, the difficulty is that when you substitute r= 0 in the fraction, you get "0/0". Do you remember any methods from Calculus I for doing that? Perhaps L'Hopital's rule? Or maybe "rationalizing the denominator" by multiplying both numerator and denominator by $\sqrt{r^2+ 1}+ 1$

thanks for the help. I got it! (one more thing, I am a grasshopper!) :)

## 1. What is a multivariable problem?

A multivariable problem is a mathematical or scientific problem that involves more than one independent variable. This means that there are multiple factors or variables that affect the outcome of the problem.

## 2. Why is it important to limit problem multivariable?

Limiting problem multivariable is important because it allows for a clearer understanding and analysis of the problem. When there are too many variables, it can be difficult to determine the exact cause and effect relationship between them, making it harder to find a solution.

## 3. How can we identify and limit multivariable problems?

The first step in identifying and limiting multivariable problems is to clearly define the problem and all of its variables. Then, we can use techniques such as simplification, controlling variables, and statistical analysis to limit the number of variables and focus on the most important ones.

## 4. What are some common challenges with multivariable problems?

Some common challenges with multivariable problems include accurately measuring and controlling all variables, identifying and accounting for any confounding variables, and determining the most important variables to focus on.

## 5. Can we completely eliminate multivariable problems?

No, it is not always possible to completely eliminate multivariable problems. However, by limiting the number of variables and controlling for potential confounding factors, we can make the problem more manageable and increase our chances of finding a solution.

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