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Joydeep B
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what is the ε & δ definition of continuity of f(x) at x=0
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.
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.
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.
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.
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.