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.
PROBLEM 2 (25 Points) Determine the Taylor series representation centered at x = 2 _{ } of
3 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.
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) _{
}
B)
(16 Points) _{
}
C) (16
Points) _{
}
D) (17
Points) _{
}
(Determine if the series converges absolutely, conditionally, or diverges.) 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)
