# Find the domain of continuity of this function

• chrisy2012
In summary, the domain of continuity for the given function is the xy plane excluding the point (0, 0). This is the same as the overall domain of the function.
chrisy2012

## Homework Statement

x*sin(sqrt(x^2+y^2))/sqrt(x^2+y^2)
find the domain of continuity

none

## The Attempt at a Solution

I found the domain, which is x^2+y^2 > 0 and since x^2 >= 0 and y^2 >= 0 therefore the domain is (-inf,0) (0,inf)
but the professor then asked for the "domain of continuity" and asked us to "carefully explain", i don't know how that is different from the domain i found.

chrisy2012 said:

## Homework Statement

x*sin(sqrt(x^2+y^2))/sqrt(x^2+y^2)
find the domain of continuity

none

## The Attempt at a Solution

I found the domain, which is x^2+y^2 > 0 and since x^2 >= 0 and y^2 >= 0 therefore the domain is (-inf,0) (0,inf)
That's not the domain. As you have it, the domain is all of the real line except 0. Your function has a domain that is two-dimensional; i.e., the domain is actually some subset of R2.
chrisy2012 said:
but the professor then asked for the "domain of continuity" and asked us to "carefully explain", i don't know how that is different from the domain i found.

Mark44 said:
That's not the domain. As you have it, the domain is all of the real line except 0. Your function has a domain that is two-dimensional; i.e., the domain is actually some subset of R2.

sorry my mistake, What i meant to say is that the domain is the xy plane except for at point (0,0). But still, how is that different from "domain of continuity"?

I'm not familiar with that term. Your function is defined at and continuous at every point in the plane, except (0, 0). I'm guessing that, in this case, the domain of continuity is the same as the domain.

## What is the definition of continuity in a function?

Continuity in a function means that the function is smooth and has no breaks or gaps in its graph. It also means that the function's output values change gradually as the input values change.

## What is the domain of a function?

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

## How do you find the domain of continuity of a function?

To find the domain of continuity of a function, you need to check for any breaks, gaps, or points of discontinuity in the graph of the function. The domain will be all the x-values where the function is continuous.

## What are some common types of functions with continuous domains?

Some common types of functions with continuous domains are polynomial functions, exponential functions, logarithmic functions, and trigonometric functions.

## Why is finding the domain of continuity important in mathematics and science?

Finding the domain of continuity is important because it helps us determine the validity and usefulness of a function. It also allows us to analyze the behavior of the function and make predictions about its outputs.

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