BC 1-2
Quiz #8
Name: ________________
Show all appropriate work clearly for full credit. NO CALCULATORS
Skills
1. A lamp pole is 12 feet tall. A 5 foot tall girl is walking away from the lamp pole at a rate of 6
feet per second. How fast is the girl’s shadow lengthening when she is 10 feet from the base
of the pole?
2. Evaluate the limits:
 cosh( x) 
a. lim 

x  sinh( x )


1
 1
b. lim  x
 
x 0  e  1
x
c.
lim 1  sin 4 x 
x 0
cot x
BC 1-2
Quiz #8
Name: ________________
3. Given that V  2t h , where h  h(t ) is the function graphed below, estimate the value of
dV
at t  3 . Show work/explain.
dt
4.
Consider the curve given by the parametric equations:
 x  2  3cos  2t 

 y  2sin  t 
dy
.
dx
a.
Determine
b.
Eliminate the parameter t from the parametric equations and write an equation in
terms of x and y for this curve.
BC 1-2
Quiz #8
Name: ________________
5. Use the graphs of f and g to describe the motion of a particle in the plane whose position
at time t is given by: x  f (t ), y  g (t );0  t  4 .
a. Sketch the graph of the parametric equations x  f (t ), y  g (t );0  t  4 . Label the initial
and terminal points and the direction the point travels.
b. Find the speed of the point  x(t ), y(t )  at time t 
c. Does the speed ever equal 0? Explain briefly.
1
.
2
BC 1-2
Quiz #8
Name: ________________
Concepts:
6. Determine the real number a having the property that f (a )  a is a relative minimum of
f ( x)  x 4  x3  x 2  ax  1 .
7. For all real numbers x and y, let ƒ be a function such that:
I.
f ( x  y )  f ( x)  f ( y )  4 xy  2
II.
f (0)  1
a.
Find ƒ(0). Justify.
b.
Find an explicit formula for ƒ'(x) using the limit definition of a derivative. Justify all
steps.
c.
Find an explicit formula for ƒ(x).
BC 1-2
Quiz #8
Name: ________________
8. An inverted cone has height 10 cm and radius 2 cm. It is partially filled with liquid,
which is oozing through the sides at a rate proportional to the area of the cone in contact
with the liquid. Liquid is also being poured into the top of the cone at the rate of
1 cm3/min. When the depth of the liquid is 4 cm, the depth is decreasing at a rate of
0.1 cm/min. At what rate should liquid be poured into the top of the cone to keep the
liquid at a constant depth of 4 cm?
[The lateral surface area of a cone is  rhs , where hs  slant height ].