Transcription of LIMITS AND CONTINUITY - University of Pennsylvania
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LIMITS AND CONTINUITY - University of Pennsylvania
2/19/20131 Math 114 Multivariable and ContinuityIn this section, we will learn about: LIMITS and CONTINUITY of various types of 114 Multivariable LimitsLIMITS AND CONTINUITY Let s compare the behavior of the functions as x and y both approach 0 (and thus the point (x, y) approaches the origin).22222222sin()( , )and( , )xyxyf x yg x yxyxy+ ==++Math 114 Multivariable LimitsLIMITS AND CONTINUITY The following tables show values of f(x, y) and g(x, y), correct to three decimal places, for points (x, y) near the 114 Multivariable LimitsLIMITS AND CONTINUITY This table shows values of f(x, y).Table 1 Math 114 Multivariable LimitsLIMITS AND CONTINUITY This table shows values of g(x, y).Table 2 Math 114 Multivariable LimitsLIMITS AND CONTINUITY Notice that neither function is defined at the origin. It appears that, as (x, y) approaches (0, 0), the values of f(x, y) are approaching 1, whereas the values of g(x, y) aren t approaching any 114 Multivariable LimitsLIMITS AND CONTINUITY It turns out that these guesses based on numerical evidence are correct.
14.2 Limits and Continuity In this section, we will learn about: Limits and continuity of various types of functions. Math 114 – Rimmer 14.2 – Multivariable Limits LIMITS AND CONTINUITY • Let’s compare the behavior of the functions as x and y both approach 0 (and thus the point (x, y) approaches the origin). 2 2 2 2
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