M127H Fall 2009
Quiz # 7 10/30 /2009 Solutions
Problem 1 (10 points): The surface area A of a spherical cell of radius r is
proportional to the square of the radius. That is:
A(r) = Kr2 ,
where K is a positive constant. If you can determine the radius wit
M127H Fall 2009
Quiz # 6 10/23 /2009 Solutions
Problem 1 (10 points): Find the second derivative of
f (x) = x ebx
where b is a positive constant.
f (x) = ebx b x ebx = (1 bx) ebx
f (x) = bebx b (1 bx) ebx = (b2 x 2b) ebx
Problem 2 (5 points): Find the der
M127H Fall 2009
Quiz # 5 10/19 /2009 Solutions
Problem 1: Find all points in the graph of
f (x) = (x + 1)2 (2x 3)3 ,
where the tangent line is horizontal.
If the tangent line is horizontal at (x0 , f (x0 ) then f (x0 ) = 0. We begin by
nding the points wh
M127H Fall 2009
Quiz # 4 10/9 /2009 Solutions
Problem 1: Find all points on the curve y = 4 x2 , whose tangent line is
parallel to the line y = x.
Solution: We need to nd the points in the graph where the tangent line has
slope 1. The slope of the tangent
M127H Fall 2009
Quiz # 2 9/25/2009 Solutions
Problem 1: The half-life of C 14 is 5730 years. Suppose that wood found at
an archeological excavation site contains about 35% as much C 14 (in relation to
C 12 ) as living plant material. Determine when the wo
M127H Fall 2009
Quiz # 1 9/18/2009
SOLUTIONS
Problem 1: Simplify the following expressions as much as possible:
2 )
a)
e2 ln x = eln(x
= x 2
b)
log3 9x = x log3 9 = 2x
c)
log2 (2x2 1)
ln(2x2 1)
= 0 since:
ln 2
ln u
log2 u =
ln 2
Problem 2: Two quantities