1. (24 points) De termine whether each statement is true
(T) or false (F), then CIRCLE the
appropriate response. Assume that x and y are positive .
T
F
T
F
F
F
T
F
2. (20 points) A watermelon is heaved into the air at a
velocity of 16 ft/s upwards, from atop a
cliff that is 96 feet above ground. As sume the accele ration due to gravity is
−32 feet/s2.
Let s(t) denote the height of the watermelon above the ground, as a function of
time t.
Let v(t) denote the velocity of the watermelon, as a function of time t.
a. Write (or derive) an equation for v (t).
Solution :
the initial velocity which is unknown .
b. Write (or derive) an equation for s(t).
Solution:
because s(0) = 96 since we start 96 feet off the ground.
c. In how many seconds will the watermelon strike the ground? (Show your work.)
Solution: We need to solve for t where s(t) = 0. 0 = s(t) = −16t2 + 16t + 96 =
−16(t − 3)(t + 2), so t = 3 or t = −2, but time runs forward so t = 3 seconds.
d. What is the velocity of the watermelon when it strikes the ground? (Show your
work.)
Solution: v(3) = −32(3) + 16 = -80 feet/second.
3. (10 points) Find the function f(x) which has the fol lowing properties :
Solution: 
we get 
Then
we get 
4. (10 points) Find the equation of the line tangent to
y = x ln x
at x = 2.
Solution: First y(2) = 2 ln 2. The general (point-slope) equation for the line
is y − 2 ln 2 = m(x − 2) where m is the slope , which is given by y'(2). We find
y' = 1 + ln x so y'(2) = 1 + ln 2. Then y − 2 ln 2 = (1 + ln 2)(x − 2) .
5. (16 points) There were 320 students in lecture this week. In 3 weeks, there
are expected to
only be 240 students attending lecture. (tsk!) Assuming exp onential decay ,
estimate how
many students will be coming to lecture in 9 weeks. ( Simplify your answer as
much as
possible).
Solution: 
and we need to find A(9) so we first must find k. We are
told 320 = A(0) = P so 
Also
( which is negative ).
Then 
so 135 students.
6. (30 points) Evaluate the following (four—turn the page over!) indefinite
integrals. Simplify
your answers as much as possible. Show your work. You may use u- substitution ,
trig
formulas , the simple power rule , the fundamental theorem of calculus, etc.
a.
Solution: 
letting u = tan x.
b.
Solution: 
letting u = ln(3 + 7x).
c.
Solution: 
using the simple power rule.
d.
Solution: 
letting u = (ln(2x) + 20).
