Functions, Limits, and Continuity

A function y = f(x) is a rule that assigns a nnique value of y for each of the given values of x in the definition of a domain of /, and x is said to be an independent variable and y the dependent variable. There may exist more than one value of x for a given value of y. The set of values of x is called the domain of a function, and the corresponding set of y is called the range of a function. 

The limits follow simple arithmetic operations, e.g., the sum of the limits is the limit of the sums, etc. A function is said to be continuous at Xq if 

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