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Let g : R → R be defined by Jx2 + x, if x is rational g(x) 10, otherwise. The function g is continuous at two points; what are they? For one of the points a you identified in part (b), verify that g is continu- ous at a. (This part requires very little calculation. There are two cases, a +h e Q and a +h ¢ Q. In part (a) you already did the work for the harder one of these!)

Let g : R → R be defined by Jx2 + x, if x is rational g(x) 10, otherwise. The function g is continuous at two points; what are they? For one of the points a you identified in part (b), verify that g is continu- ous at a. (This part requires very little calculation. There are two cases, a +h e Q and a +h ¢ Q. In part (a) you already did the work for the harder one of these!)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(b) Let g : R → R be defined by Ja² + x, if x is rational g(x) = 0, otherwise. The function g is continuous at two points; what are they? (c) For one of the points a you identified in part (b), verify that g is continu- ous at a. (This part requires very little calculation. There are two cases, a + h e Q and a + h ¢ Q. In part (a) you already did the work for the harder one of these!)
Transcribed Image Text:(b) Let g : R → R be defined by Ja² + x, if x is rational g(x) = 0, otherwise. The function g is continuous at two points; what are they? (c) For one of the points a you identified in part (b), verify that g is continu- ous at a. (This part requires very little calculation. There are two cases, a + h e Q and a + h ¢ Q. In part (a) you already did the work for the harder one of these!)
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