maths second question 2. (5 marks) Consider the function f: R → R defined byx if x E Qf(x) =|0 if x €R\Q.(a) (0 marks) Attempt to draw the function.(b) Prove that f is continuous at 0.(c) Let r € Q\ {0}. Prove that f is discontinous at r. Carefully state any results which you usefrom the course.(Hint: Try the case where a = 1 first; it might give you an idea of how to approach thegeneral case. Partial marks awarded if you only prove it when a = 1.)(d) (Bonus question) Let r e R\Q. Prove that f is discontinuous at r. [This question isworth 0 marks, but can make up for upto 2 marks lost elsewhere in this assignment.]

We will solve all the (b), (c), and (d)

2. (5 marks) Consider the function f : R → R defined by Sr if z€ Q S(x) = 10 if reR\Q. (a) (0 marks) Attempt to draw the function. (b) Prove that f is continuous at 0. (c) Let r € Q\ {0}. Prove that f is discontinous at r. Carefully state any results which you use from the course. (Hint: Try the case where r = 1 first; it might give you an idea of how to approach the general case. Partial marks awarded if you only prove it when r = 1.) (d) (Bonus question) Let r € R \ Q. Prove that f is discontinuous at z. [This question is worth 0 marks, but can make up for upto 2 marks lost elsewhere in this assignment.]

2. (5 marks) Consider the function f : R → R defined by Sr if z€ Q S(x) = 10 if reR\Q. (a) (0 marks) Attempt to draw the function. (b) Prove that f is continuous at 0. (c) Let r € Q\ {0}. Prove that f is discontinous at r. Carefully state any results which you use from the course. (Hint: Try the case where r = 1 first; it might give you an idea of how to approach the general case. Partial marks awarded if you only prove it when r = 1.) (d) (Bonus question) Let r € R \ Q. Prove that f is discontinuous at z. [This question is worth 0 marks, but can make up for upto 2 marks lost elsewhere in this assignment.]

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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