I need an example of a function.

In summary, a function f:R2-->R can be continuous at (0,0) with partial derivatives in (0,0), but not differentiable at that point. An example of such a function is f(x,y)=x1/3y2/3+y1/3x2/3.
  • #1
paalfis
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Member warned about not using the homework template
Give an example of a function f:R2-->R , continuous in (0,0), with partial derivatives in (0,0), but not differentiable in (0,0).

I was thinking in something like f(x,y)=IxyI
 
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  • #2
What is the definition of continuous function at a point like (0, 0) ?
 
  • #3
limit as (x,y)->(0,0) of If(x,y)-f(0,0)I=0
 
  • #4
I know what this properties mean, I just can't think of a function with partial derivatives in (0,0) but not differentiable in that point.
 
  • #5
Actually, I think that the function f (x , y) = x1/3y2/3+y1/3x2/3 works fine, am I right?
 
  • #6
Yeah that seems to work. I plotted it here.

image.jpg


image.jpg
 

1. What is a function?

A function is a mathematical concept that relates two or more quantities, often represented by variables, and produces a unique output for each input. In programming, a function is a block of code that performs a specific task when called.

2. How do I write a function?

To write a function, you first need to determine the input parameters and the desired output. Then, you can use a programming language to define the function using a specific syntax, such as the def keyword in Python or the function keyword in JavaScript.

3. Can you give an example of a simple function?

One example of a simple function in mathematics is the quadratic function f(x) = x^2 + 2x + 1, where the input is x and the output is f(x). In programming, a simple function can be something like add(x, y), which takes two numbers as inputs and returns their sum.

4. What is the purpose of a function?

The main purpose of a function is to break down complex tasks into smaller, more manageable parts. This allows for more efficient and organized coding, as well as easier debugging and maintenance of code. Functions also promote code reusability, as they can be called multiple times in different parts of a program.

5. Can you explain the difference between a function and a method?

In programming, a function is a standalone block of code that performs a specific task, while a method is a function that is associated with a specific object or class. Functions can be used in any part of a program, while methods are typically called on an object or class instance. Additionally, methods can access and modify the attributes of an object, while functions cannot.

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