What is the ε & δ definition of continuity of f(x) at x=0?

In summary, functions of several variables are mathematical relationships between multiple independent variables and a dependent variable, which can be represented as equations, graphs, or tables. They are different from single-variable functions as they have multiple independent variables and have various applications in fields such as physics, engineering, economics, and biology. To graph a function of several variables, a three-dimensional coordinate system or contour plots can be used. A partial derivative is the rate of change of a function with respect to one of its independent variables, while holding all other variables constant.
  • #1
Joydeep B
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what is the ε & δ definition of continuity of f(x) at x=0
 
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  • #2
It is the same as for any other x0.
 

FAQ: What is the ε & δ definition of continuity of f(x) at x=0?

1. What are functions of several variables?

Functions of several variables are mathematical relationships between multiple independent variables and a dependent variable. They can be represented as equations, graphs, or tables and are used to model real-world phenomena.

2. How are functions of several variables different from single-variable functions?

Unlike single-variable functions, which have only one independent variable, functions of several variables have multiple independent variables. This means that the output of the function can vary depending on the values of all the independent variables.

3. What are the applications of functions of several variables?

Functions of several variables have various applications in fields such as physics, engineering, economics, and biology. They can be used to model complex systems, optimize processes, and make predictions about real-world phenomena.

4. How do you graph a function of several variables?

To graph a function of several variables, we use a three-dimensional coordinate system where the x-axis, y-axis, and z-axis represent the values of the independent variables and the output of the function is represented by the height of the graph. We can also use contour plots to visualize functions of several variables.

5. What is a partial derivative in functions of several variables?

A partial derivative is the rate of change of a function with respect to one of its independent variables, while holding all other variables constant. It measures how the output of the function changes when we vary one of the independent variables while keeping the others fixed.

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