BC 1
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1.
Name:_________________
Find each limit. No work required.
a.
c.
2.
Quiz #2
 x2  7 
lim 

x 3 
 x  3 
lim  x 

x0
 2  2x  4 
b. lim 

x  5  3 x  7 


d. lim
x 
3x 4  2 x 2  1
6 x2  2 x4
Find the limit algebraically. Clearly show how you arrived at your answers. An answer without
any algebraic justification will receive little or no credit.
 x  3
lim 

x 9  9  x 
1
3. Use the Intermediate Value Theorem (IVT) to help determine if f ( x)  x 3  x 2  1 has a root on the
3
interval [1,3]. You need not find any roots, but be explicit in stating how IVT helps you determine
whether or not there is a root on [1,3]. You may assume that f is continuous.
BC 1
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Quiz #2
Name:_________________
4. Suppose y  3  4 x 2 for x  [1,1] and y (1)  1 . Sketch y (actual) on the first set of axes (using - - - ).

Then, using a step size of 0.5, construct the graphs and the piecewise-defined functions for yapprox
(graph
using
) Sketch the graph of yapprox on the second set of axes, be sure to put scales on the axes and mark
and label your endpoints clearly.
yapprox














yapprox













BC 1
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Quiz #2
Name:_________________
5. 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 (5)  0 .
6. Let f ( x ) 
1
. Find f (2) using the limit definition of the derivative.
x 3
2
BC 1
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7.
Quiz #2
Refer to the graph of f  (not
) shown at the right to answer
the following questions.
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 (1)  2 , write the equation of the tangent line to the graph of f at x  1 .
f.
Rank the numbers f (2), f (1), f (2) and f (4) in increasing order. Briefly explain you
reasoning.
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