II. Applications/Analysis (Technology allowed, show all work! !) 1. A cup of hot chocolate has temperature 80 C in a room kept at 20 C. After half an hour, the hot chocolate cools to 60 C. Knowing this: a) What is the temperature of the hot chocolate after another half hour (4 points)? b) After about how long will the hot chocolate have cooled down to 40'C (3points)? 2. Find the Maclaurin series (in summation form) for the exponential function f (x) = 2*(5 points).3. Determine if the following series converges or diverges, using either the Ratio Test or oat Test (4 points): \"'3 _ 2a 2225;" n 1 4. Use Taylor's Inequality to estimate the aeearaqp of the 5*'1 degree Taylor polynomial approximation to the function f(x) = sin (I), centered at x = E, when 0 5 x 5 6 points). 5. Compute the iimit, showing all steps (don't just say the technology did this problem for you) of the following sequence (4 points): ajrt =1J9n2 +4n3n