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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.