Future Value

This quiz contains problems as seen in Sections 5 through 9. You are only allowed to use your

book, notes, and the instructor as resources. You are not allowed to work with other

students. Please show all work. Problems without work will receive no credit. Problems are to

be done on a separate piece of paper to be handed in at the beginning of class. Your assignment

must be clean, neat, stapled, and without “frills” on the end of the paper. You will lose credit if

your work does not follow these rules!

1. You want to invest $450 for 5 years, with interest compounded continuously. What interest

rate would you need to achieve a future value of $550? Give the exact value as your answer.

Do not use a calculator. (1 point)

2. Evaluate the following limits. (4 points)

(a) lim

x??3

(ln (2x + 25))

(b) lim

x?9



x ? 9

?

x

2 ? 81

(c) lim

x?1/2



4x

2 + 4x ? 3

2x

2 + 15x ? 8



(d) lim

x?5?



x

2

5 ? x



3. Use the definition of the derivative to find the derivative of f(x) = x + 1

x ? 1

. Then, determine

the instantaneous rate of change when x = 2. (3 points)

4. Given the function g(x) =

?

??

??

5x

2 + 1 if x < 0

2

x

if 0 < x < 1

4 if x ? 1