Make sure you understand questions appeared in Exam1,2, Quiz 1-4 and Hw1-12, then try the following:

Ex1.1, #13, Ex1.2, #1, Ex1.3 #5;
Ex2.1,#15(what is the relation of 1/a,1/b for general 
a, b), Ex2.2,#11,Ex2.3#4;

Ex3.1#6c,  Ex3.2#15,Ex3.3#7,Ex3.4#13,Ex3.5#13,Ex3.6#4b,Ex3.7#3b;

Ex4.1#9c, 11bd, Ex4.2,#4;
Ex5.1#3, Ex5.2#7,11, Ex 5.3, #4, Ex 5.4, #4,8,9;

Ex 6.1 #2, Ex 6.2 #7;

Ex 7.1 #5, 9, Ex 7.2, #1, 3, 8, 16, Ex7.3 #5, 6.

Find examples of function f on [0,1] such that

(i) f is bounded but not Rieman integrable.

(ii) f is Rieman integrable but not continuous on [0,1].

(iii) f is Rieman integrable but not continuous on (0,1).

(iv) f is continuous on (0,1) but not uniformly conitunous on (0,1).

(v) f is uniformly continuous on (0,1) but not differentiable on (0,1).