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Question: goals the goals of this assignment are 1 to understand...

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Goals: The goals of this assignment are 1. to understand how to tell if a limit exists algebraically, numerically, and graphically, and to practice communicating mathematical ideas in writing. Instructions: Hand in a final draft. (That assumes you make a rough draft, correct the mathematics, perfect your sentences, and then write up your final on a separate piece of paper from your rough draft.) Address each part of each question in order, and label your answers with the numbers and letters of the parts you are addressing. Strive for clarity, neatness and legibility. It helps to use a sharp pencil and an eraser. 1. Consider the funtion a() (a) Draw a graph of a(e) for -5 5. There is a point between -5 and 5 which is not in the domain of a(x). Make sure this is clear in your graph. (b) Use your graph from part (a) to estimate lim, a(z) Explain your reasoning in a sentence. (c) Use your graph from part (a) to estimate lim a(r). Explain your reasoning in a sentence. (d) Use algebra to rewrite a(x) so that you can compute the exact value of lim az) L. Explain your reasoning (e) Use the algebra from part (d) to compute the exact value of lim a ) M. Explain your reasoning. ) Create a table of values of afe) that support your claim that lim a) L. You should inelude at least 4 values of x in the table, and you should be sure to look at values on both sides of-3. (8) Create a table of values of a(x) that support your claim that lim al) M. You should include at least 4 values of x in the table, and you should be sure to look at values on both sides of 2 (h) Joe looks at the graph of the function on his calculator and says The lim a(r) exists because the graph of a(x) is just a line. Katie says I used algebra and found there is hole at r 2, so there isnt a limit. Is either of them correct? Explain. 2. What is wrong with the following argument? Explain your reasoning in complete sentences. The function z(t) has domain |-5,5). Some values of z(t) are shown in the table below. 4.9 4.99 4.999 5.3598 5.3529 -53529-. Since the values of z(t) approach-53529 as t goes to 5 z(t) Ⅱ- lim z(t)-5.3529 3. Give an example of a function g for which lim g(x) does not exist. Then explain why the limit does t-+2019 not exist
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