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.

Printable Key

PROBLEM 1  Please answer the following true or false.  If false, explain why or provide a counter example.  If true explain why.

1.  (15 Points)  If    then    converges
   
   
   Solution
   
   

2. (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
 

  Solution

PROBLEM 3  (25 points)

Determine the radius and interval of convergence of

  Solution

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. 

1. (15 Points)  Determine the Maclaurin series for f(x) .
   
   Solution
   

2. (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)