BC 1
Problem Set #2
Due Friday February 7
Name:
Please show appropriate work – no big calculator leaps – except as indicated. Work should be shown
clearly, using correct mathematical notation. Please show enough work on all problems or explain
clearly (unless specified otherwise) so that others could follow your work and do a similar problem
without help. Collaboration is encouraged, but in the end, the work should be your own.
1.
Let f  t   24  4t for t  0.
a.
b.
Let D(x) be the function that gives the distance from the point (2, 9) to the point (x, f(x)).
i.
Find a formula for D(x).
ii.
Use the "min" button on your calculator to find the minimum value of D and the value
of x where this value occurs, correct to 3 decimal places.
Let A(x) be the function that gives the area of the trapezoid bounded below by the t-axis, on
the left by the y-axis, above by the graph of y = f(t), and on the right by the line t = x.
i.
Find a formula for A(x).
ii.
State the domain and range of A.
 A( x)  A(t ) 
iii. Evaluate: lim 

x t
xt

iv.Fill in the blank with Wow! or something similar:
BC 1
Problem Set #2
Due Friday February 7
Name:
3. The graphs of f and g are shown at right. Evaluate the following limits (estimate as closely as possible
when necessary). Write DNE if the limit does not exist. No work or explanation required.
y = f(x)
a. Lim( f ( x))
x2
f ( x))
b. Lim(

x 0
f ( x))
c. Lim(

x 0
d. Lim( f ( x))
x 0
e. Lim( f ( x)  g ( x))
x 0
f.
Lim( f ( x)  g ( x))
x 0
For g. and h. give a brief
explanation for your answer:
 f (4  h)  f (4) 
g. Lim 

h 0
h


 g ( x) 
h. Lim 

x 3
 x3
y=g(x)
BC 1
Problem Set #2
Due Friday February 7
4. Evaluate the following limits:
 1

 x2 1 
a. Lim 

x 1
 x 1 


 3 x 2
b. Lim 

x 8
 x 8 
Name: