MATH 107  PRACTICE MIDTERM 1   Please work out each of the given problems.  Credit will be based on the steps that you show towards the final answer.  Show your work.   PROBLEM 1  Please answer the following true or false.  If false, explain why or provide a counter example.  If true explain why.  (15 Points)  If    then    converges Solution (15 Points)  Let  then if x = 0  is in the domain of  f , then x = 4  is also in the domain of  f. Solution     PROBLEM 2  (25 Points)  Determine the Taylor series representation centered at x = 2 of                 3 f(x)  =                                 4x - 7   PROBLEM 3  (25 points) Determine the radius and interval of convergence of         PROBLEM 4 For a Normal Distribution (Bell curve) the integral          represents         P(0 < z < x) the probability that an event will lie between 0 and x.  (15 Points)  Determine the Maclaurin series for f(x) . Solution (15 Points)  Find P(0 < z < 1) accurate to two decimal places and explain why you are assured of this accuracy. Solution PROBLEM 5   Determine if the following series converge or diverge.  Explain which test(s) you are using and show all your work. A)    (16 Points)  Solution B)    (16 Points)    Solution C)   (16 Points) Solution D)   (17 Points)            (Determine if the series converges absolutely, conditionally, or diverges.) Solution   Extra Credit:  Write down one thing that your instructor can do to make the class better and one thing that you feel should not be changed. (Any constructive remark will be worth full credit)