Let g be a function with domain the rational numbers, defined by g(x) = 2/( x - sqrt(2)) for rational x. a. Sketch the graph of g as well as you can, keeping in mind that g is only defined at rational points. b. Use the general definition of a limit to prove that limx-->0 g(x) = -sqrt(2). c. Prove that g is continuous at the point x = 0 by showing that the limit in part (b) equals g(0). d. Is g continuous at other points of its domain?

Let g be a function with domain the rational numbers, defined by g(x) = 2/( x - sqrt(2)) for rational x. a. Sketch the graph of g as well as you can, keeping in mind that g is only defined at rational points. b. Use the general definition of a limit to prove that limx-->0 g(x) = -sqrt(2). c. Prove that g is continuous at the point x = 0 by showing that the limit in part (b) equals g(0). d. Is g continuous at other points of its domain?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.1: Polynomial Functions Of Degree Greater Than

Problem 36E

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