Written homework is intended to help students develop their communication and exposition skills through complete write-ups of inclass team problems. While cor- rectness of the solution is, of course, necessary, much of the grade for the problem is dependent on clear and appropriate exposition. Convincing someone that your answer is correct is equally as important as nding the correct answer! Exposition shall be appropriate for the type and level of the problem. One principle we use is that exposition should be detailed around the main aspects of the problem, but terse exposition is appropriate for subsidiary parts of a problem. As an example: If the problem asks you to nd the derivative of f(:13), then you would need to describe the rules you use to do so and justify that they apply in the given situation. But if you are asked to nd the largest value of f(:L') in an interval using the second derivative test, then calculating f'(a:) will be but one step in the larger process, and thus does not need an indepth explanation on its own. Answer each of the following questions, justifying your answers fully with complete sentences. You must fully justify each limit value that you use with either the 56 denition of limits, or by using limit rules that we covered for Wednesday. 1. Consider the limit lim 9:2 tan(sc) 31*}0 (a) Hypothesize what the value of the limit is, and describe why you chose that value. (b) Calculate the limit's value. (c) Does the value you found match your hypothesis? 2. Without calculating the value, describe a strategy you would use to compute the following limit: 2 2 1 lim sin(:c) $~>1 :L' 7 1