Question 3. Tables. Reconstruct the sentence, table and caption shown below. To label the table, use \labelftab: Math2024tasks) after the caption line. To make the cross- reference to "Table 1" in the sentence before Table 1, use efftab: Math2024tasks). The information in Table 1, including the weeks when tasks are due, is drawn from the Math 2024 Course Outline. Table 1: Tasks for Mathematical Communication (Math 2024). Math 2024 assessment tasks Category Content Assignments Mathematical Paper Minitalks 1. Mathematical Typesetting 2. Cultural Awareness 3. Good Mathematical Writing 4. Career Planning Talk 1: 5 minutes Draft of written paper Written paper Talk 2: 10 minutes HMC Math Fun Facts Week due Week 6 Week 8 Week 10 Week 11 Week 4 Week 7 Week 12 Week 13 throughout Question 4. Good Problems 1: Layout. Choose an assignment question, or part of a question, from another maths course you're taking in this study period. If you haven't been given any assignments yet, then use a question from one of your courses from a previous study period. (Even if your other courses are not in maths, choose a question with some technical content including symbols if possible.) (a) Type up your solution in INTEX, using the guidelines from the Good Problems handout on Layout. (b) Include the course name, the assignment name, and the study period and year. State the full question at the start of your answer. (c) Your answer should be 1/2 to 1 pages of typed text; otherwise marks will be deducted. If you have more text than that, then omit part of your assignment question (and answer). Hint: It's faster to write a clean copy by hand first, then transcribe it into INTEX. Question 6. Good Problems 3: Mathematical Symbols. Reproduce parts (a)-(e) below in LATEX, using the guidelines from the Good Problems handout on Mathematical Symbols. Hint 1. To produce the symbol N, use the command \mathbb (N). This command re- quires the amsfonts package. You can load this package by including the line \usepackage{amsfonts) in the preamble. Hint 2. In part (a), the symbol C requires the amssymb package. Hint 3. In the third displayed formula in part (a), to produce the word and in roman font and well spaced, use \qquad \text{and) \qquad. The command \text requires the amsmath package. Hint 4. You can find many of the symbols below among the icons under the tabs ("Math, Greek, Symbols,...") at the top of the WinEdt window. (a) The set N of natural numbers forms a subset of the set Z of integers, and so on: NCZCQCRCC. The number 3.14 is an element of the open interval (3,5), which in turn is a subset of the half-open interval (3,5) and the closed interval [3,5]: 3.14 (3,5) c (3,5) C (3,5). Note that since 3 (3.5) but 3 (3,5), we actually have (3.5) C (3,5). Also (3,5) = [3,5) (3,5) and [3.5) (3,5) U (3,5). # (b) The composition of two functions f and g is denoted by fog. For example, if f(2)= cos z and g(x)=r, then fog(x) = cos(r) while gof(x) = (cos r) = cos r. (c) The number "six factorial" is approximately 700, since 61-6-5-4-3-2-1 =720 = 700. (d) The floor [3.14] of 3.14 is the largest integer less than or equal to 3.14, so [3.14] = 3. In particular [3.14] Z and [3.14] 3.14. The ceiling [3.14] of 3.14 is 4. (e) For the function f(x)=1/(x-2), we have lim f(x) = +00 while