Problem 3.6. Given two different real numbers A, B, consider the fol- lowing function: 1 if Db\") = A - :1: E Q A + 1 if :1: i Q. Calculate the upper and lower Riemann sums based on an arbitrary partition P = {$0, . . . , 3.3,} of [c, d]. Explain how do you use the density phenomenon of real numbers in your calculations. Problem 3.7. Consider the function f , where 11:3 if x E [1, 5.5) f@)_{ seepsnm. and take the partition P = {1,5, 6, 7, 20}. Compute the upper and lower Riemann sums of f for the partition P. Problem 3.8. Consider the function f, where _ 3x if m E [0, 5) {2 nmewnn and take the partition P = {0, 3, 4, 11}. Compute the upper and lower Riemann sums of f for the partition P. Problem 3.9. Consider the function f, where m Hmem) f(a:)= 10 if:1:=7 2x Hme and take the partition P = {0, 1, 4, 10, 11, 12}. Compute the upper and lower Riemann sums of f for the partition P. Problem 3.10. Consider the function f, where _ :52 ifxEQ m_{3sxeo Calculate the upper and lower Riemann sums based on an arbitrary partition P = {$0, . . . , 3.3,} of [0, 1]. Explain how do you use the density phenomenon of real numbers in your calculations. Problem 3.11. (The Glossary: Definitions and Theorems) State precisely the following definitions and theorems. (1) A function f is bounded.. (2) The Ordinate set of a function over an interval.. (3) A partition over an interval. (4) A special partition of an interval in equal parts. (5) The Superior value of a function over an interval. (6) The Inferior value of a function over an interval. (7) The Superior Rectangle of a function over an interval. (8) The Inferior Rectangle of a function over an interval. (9) The Upper Riemann Sum of a function over a Partition. (10) The Lower Riemann Sum of a function over a Partition. (11) The Density Phenomenon of Reals