BC 1
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1.
Name:_________________
Find each limit. No work required.
a.
c.
2.
Quiz #2
 7  x2 
lim 

x 3 
 x  3 
lim  x 
x 4 
 2  3x  4 
b. lim 

x  5  3x  7 


d. lim
x 
3 x3  2 x 2  1
2 x4  6 x2
Find each limit algebraically. Clearly show how you arrived at your answers. An answer without
any algebraic justification will receive little or no credit.
a.
 x2  2 x  3 
lim 

x 3 
 x  3 
b.
 5

 x 1  5 
lim 

x 2
 2 x 


BC 1
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Quiz #2
Name:_________________
3. The graphs of f and g are shown at right. Evaluate the following: No work or explanation required. Be
Careful – look at the correct graph. (Write DNE if the limit does not exist).
y = f(x)
a. Lim( f ( x))
x 0
b. Lim ( f ( x))
x 3
c. Lim ( f ( x))
x 3
d. Lim( f ( x))
x 3
e. Lim( f ( x)  g ( x))
x 0
f.
Lim( f ( x)  g ( x))
x 3
y=g(x)
 f ( h)  1 
g. Lim 

h 0
h


 g ( x)  g (1) 
h. Lim 

x 1
 x 1 
BC 1
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Quiz #2
Name:_________________
4. If the function below is a velocity curve ( y  f ( x) ), sketch the displacement curve ( y  f ( x) ) on the
same set of axes. Assume f ( 3)  1.
5. Let f ( x)  x 2  5 . Find f (2) using the limit definition of the derivative.
BC 1
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6.
Refer to the graph of f  (not )
shown at the right to answer the
following questions.
Quiz #2
Name:_________________
Graph of f 
a.
For what values of x
(approximate) is 
decreasing? Justify your
answer.
b.
For what value(s) of x (approximate) does  have a local minimum? Justify your answer.
c.
For what values of x (approximate) is  concave up? Justify your answer.
d.
For what value(s) of x (approximate) does  have inflection points? Justify your answer.
e.
If f (3)  2 , write the equation of the tangent line to the graph of f at x  3 .
BC 1
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Quiz #2
Name:_________________
7. Let y  f ( x) be the function with graph shown below.
a. Give an interval for which f satisfies the Intermediate Value Property:
b. Give an interval for which f does not satisfies the Intermediate Value Property:
1
3

if x 
 k  2
3
2
8. Let f ( x)   2
. Find all value(s) of k for which f is continuous at x  .
2
 2 x  kx  12 if x  3
2
 2 x  3