Determining the set of points at which the function is continuous.

In summary, the task is to determine the set of points at which the function F(x,y) = arctan(x + √y) is continuous. The attempt at a solution involved using the chain rule, but the solution given in the back of the book involved e and other trig functions. The speaker is asked to show their attempt at solving the problem.
  • #1
SneakyG
7
0

Homework Statement


Determine the set of points at which the function is continuous.
F(x,y) = arctan(x + √y)

Homework Equations


Perhaps the chain rule?


The Attempt at a Solution


I derived it, but the solution in the back of the book is nothing like what I expected. It involves e and other trig functions.
 
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  • #2
SneakyG said:

Homework Statement


Determine the set of points at which the function is continuous.
F(x,y) = arctan(x + √y)

Homework Equations


Perhaps the chain rule?


The Attempt at a Solution


I derived it, but the solution in the back of the book is nothing like what I expected. It involves e and other trig functions.

So show us what you did.
 

1. What is continuity in a function?

Continuity in a function means that there are no abrupt changes or breaks in the graph of the function. This means that the function is defined and has a smooth, unbroken curve without any gaps or jumps.

2. How do you determine if a function is continuous?

To determine if a function is continuous, you need to check three things: if the function is defined at the given point, if the limit of the function exists at that point, and if the limit is equal to the function value at that point. If all three conditions are met, then the function is continuous at that point.

3. Can a function be continuous at one point but not at others?

Yes, a function can be continuous at one point but not at others. This means that the function may have abrupt changes or breaks at certain points, but is still considered continuous overall. An example of this is the absolute value function, which is continuous everywhere except at the point where the absolute value changes sign.

4. How do you determine the set of points at which a function is continuous?

To determine the set of points at which a function is continuous, you need to follow the three conditions for continuity: check if the function is defined at the given point, if the limit exists, and if the limit is equal to the function value. If all three conditions are met, then that point is considered continuous. This process needs to be repeated for all points in the function's domain.

5. Can a function be continuous at every point in its domain?

Yes, a function can be continuous at every point in its domain. This means that the function has no abrupt changes or breaks in its graph and is smooth and unbroken throughout. An example of this is a polynomial function, which is continuous at every point in its domain.

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