ABSTRACT
This chapter discusses the notion of limit for functions of several variables. It first presents the nonexistence of the limit at a point by the Two-path test. Next, criteria for the existence of the limit are investigated in which the Squeeze Principle plays a crucial role. The concept of the limit of a multivariable function is further used to define the continuity and the continuous extension of a several variable function. The chapter explains the main difference between single and multivariable calculus. For functions of one real variable, the existence of the limit at a point is equivalent to the fact that the two sided limits (to the left and to the right at that point) exist and are equal. All elementary functions (polynomials, rational, trigonometric, exponential and logarithmic functions) are continuous on their domain of definition. This means that one can compute their limit at a point by direct substitution.
