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Calculus I Test
#1 March 8,
2004
Name____________________ R. Hammack
Score
______
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(1)
(a) -1/2
(b)
(c) Find the domain of the function .
We can't have , or, in other words, we can't have sin(x) =,
for such values make the denominator of f 0
Now, the values of x between 0 and for which sin(x) = are and .
Of course, we could add any integer multiple of to them and still sin(x) =.
Thus the domain of f is the set
(2)
(a) Sketch the graph of the equation .
(b) Find the equation of the line that is parallel to the graph of (from Part a, above) and passes through the point . Put your final answer in slope-intercept form, and simplify as much as possible.
By point-slope formula,
(3) Suppose and
(a)
(b)
(4) Sketch the graph of a function satisfying the following properties.
, , , , , . and .
Note: It's hard to draw this graph with the program I am using.
There should be a solid dot at the point (2, 1) and a hollow dot at (2, 3).
The vertical line between these points should not be there.
(5) The graph of a function is sketched. Use this information to find the following limits.
(a)
(b) 3/4
(6) Evaluate the following limits.
(a)
(b)
(c)
(d)
(e)
(f)
(7) This problem concerns
the function
(a)
1
(b)
(c) At which x
values (if any) is the function discontinuous?
Explain your answer.
The function is not continuous at x
= 0, because, as the previous two answers demonstrate, .
Thus the definition of continuity is not satisfied.
(d) Find the horizontal asymptotes (if any) of . Be
sure to explain your work.
Note that
(Because, while the numerator is bounded between -1 and 1, the denominator grows
without bound.)
Likewise the limit as x approaches negative infinity is 0.
THUS the line y = 0 is a horizontal
asymptote.