INSTRUCTIONS: On a separate sheet of paper, write out the solutions to the following problems. Show all steps in the solution and use complete sentences when asked to give interpretations of your answers. Show all steps. If a graph does not have correct axes labeled, scale labeled, or graphs labeled it will not receive full credit. You may use calculators to check your work, but you are being graded on your algebraic work. No credit will be given to just a nal answer without supporting work. If you use outside resources (including your peers and chegg) make sure you cite them at the top of the page and put the answers in your own words with proper justication. 1. Consider the function f (w) = 2:132 7x + 9. (a) Evaluate f (0), f'(0), and f' ' (0) to nd the second-degree Taylor polynomial for f (w) centered at ac = 0. (b) Evaluate f (1), f' (1), and f' ' (1) to nd the second-degree Taylor polynomial for f (ac) centered at ac = 1. Distribute and simplify all terms. (c) What do you notice about your answers to parts (a) and (b)? 2. Find the sum of each convergent series. For example, if the series is the e\" formula, but evaluated at ac = 1, then the sum is 6'1. No work is required for these answers. You may just write the nal answer. 1 1 1 (1)" 1 _ _ _ _ _ (a) 3! + 5! 7! + + (2n+ 1)! + 100 10000 (1)\" - 102" 1 _ _ . .. (b) 2! + 4! + + (271,)! (c) 1 0.1+0.12 0.13 +--- 9 27 81 (d)1+3+i++E+ 3. Solve the following equation for w. 1+w+w2+x3+---=5