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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.