BC 1
Sample Quiz
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1.
Find each limit. No work required. (1 pt each)
a.
d.
lim
x3
x2
x 3
b. lim
x 6

x6
x6

 5 x  8, x  2
lim f  x  if f  x    2
x2

 x  3 x, x  2
c.
lim  x 

x4
e. lim
x
2. Find the equation of the tangent line to f ( x)  2 x  3 at x  3 .
2x  2
5x  6
3.
Use the graph of f  shown below to answer questions.
Estimate x-values to the nearest tenth to answer each of the following questions. (Don't
worry about being too precise. Just convince me you understand the question.)
Give a specific x-value OR an interval – whichever is appropriate for the question. Give
all possible answers.
a. On which intervals is f concave up? Explain.
b. Does ƒ have a point of inflection at x = 4? Explain.
c. For which values of x does f have relative maxima, minima? Explain.
d. Rank the four numbers f (2), f ( 1), f (0), f (1) . Explain.
4. Given the graph of y  f ( x) below, sketch the graph of y  f ( x) .
5. Given the graph of y  f ( x) below, sketch the graph of y  f ( x) .
6. Evaluate each of the following limits: (Justify your answer algebraically)
a.
 2 x 2  5x  2 
Lim 

x 2
x2


1
 3
 x2  x  2 
b. Lim 

x 2
 x2 


x 2  3x  k
, find that value of k so that lim f (x) exists. Then find the value
x2
x2  x  2
of this limit. (Show work.)
7. If f (x) 
8.



Given f ( x)  



ax  1 ,
2x  a ,
if x   2
if  2  x  0
2
,
( x  2) 2
if 0  x
Evaluate each limit. (Write DNE if limit does not exist). Some of these limits will
involve the constant a.
a. Lim f ( x) =
b. Lim f ( x) =
c. Lim f ( x) =
d. Lim f ( x) =
x 0
x 2
e.
Lim f ( x ) =
x 2
x 0
x 2
f. Lim f ( x ) =
x 2
g. Find all values of a (if any) for which f is continuous at x  2 .
h. Find all values of a for which f  is continuous x  2 .