IMSA
MI-4
Prob. Set #3
DUE: Friday, September 11
Fall 2015
As usual, unless indicated otherwise, calculator use should be limited to computing values of functions.
1)
A superball is dropped from a height of h feet, and left to bounce. The rebound ratio of the ball
is r. For example, if r = .75, the ball bounces to ¾ the height from which it is dropped. In terms of
r and h, find formulas for
a) the height of the ball at the top of the nth bounce.
b) the total distance the ball travels assuming it bounces indefinitely. Caution: consider both the
distance traveled up and down.
2)
(You are encouraged to use your calculator’s sequence mode in this problem). In problem set #2
you explored the Fibonacci sequence with your calculator. Consider a similar sequence:
L: 5, 2, 7, 9, 16, 25, 41, …
a) State the 50th term of this sequence.
L
b) Let Gn  n 1 , for n  1. Find G20 . Give your answer to 6 decimals.
Ln
c) Explore the sequence Gn further. What appears to be lim Gn ?
n 
3)
Write each of the following in expanded form and state the sum. In your answer it is OK to use
a
a!
…... in expanded form. Recall    C (a, b) 
.
(a  b)! b !
b 
8
a)
  1
n 0
n
9 
 
n
9
b)
  1
n 0
n
10 
 
n 
10
c)
  1
n 0
n
11
 
n 
d) Generalize your result.
4)
Solve for ( x, y ) given x and y are positive integers:
1 2  3

1 2  3
x y
.
2
Sorry, no calculator for this one!
5)
Determine the range of each of the following functions. Clearly justify your result.
a.


y  3sec  x    5
3

b.


y  5sin  x    2
3

PS 3.1
IMSA
6)
MI-4
Prob. Set #3
DUE: Friday, September 11
Fall 2015
 x  12 tan(t )
a. Using a computer graphing program, graph of P(x,y) = 
where 0  t  2 . Print
 y  12sec(t )
and attach your graph to your answer sheets.
b. Is the resulting graph the graph of a function? Explain.
c. Suppose instead that x  a  tan(t ) in the above while y stays the same, and a varies in the range
0  a  20 . As the value of a changes, the graph changes. Describe how changing the value of a
changes the graph. Be as specific as possible.
7)
If the graph of f (x)  16 x contains the points A(a,5) and B(b,20) , find the exact value of the slope
of AB . Show non-calculator work!
8)
Determine the set of all real x where 0 < x < 2  , such that 4sin(x) – 3 > 0. (Show your thinking.)
State the x values of the interval to two decimal places.
9)
Find the value of x such that x = 2 
1
1
2
2
2
1
1
where … indicates that the pattern continues indefinitely. State answer exactly.
(Hint: what is in the denominator of the first fraction?)
10) Let an  (1  i ) n , where i  1
a) Write out an n1 . You may use your calculator to do this.
12
b) State two patterns you observe.
11) a) Solve for a and b:
6
a
b
.


n
n2
n  2n
2
6
b) Find the exact value of

n 1

c) Find the exact value of

n 1
6
(show thinking)
n  2n
2
6
(show thinking)
n  2n
2
n
12)
Solve for n algebraically, showing your steps.
 (4k  3)  663.
k1
PS 3.2