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Calculus I                                            Test #1                          October  5, 2004

Name _________________          R. Hammack                              Score______
Directions. Answer in the space provided. Show as much work as is reasonable.
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(1)
(a)

(b)

(c)    Suppose  ,  and .  Find .
Suppose for the moment that the problem were  .
Since , we get a triangle that looks like this.

Then .
However, in this problem is in the second quadrant, the answer is

(d)   Find all solutions of the equation

From the unit circle, you can see that the solutions are , where n is an integer.

(2) Suppose     and   .

(a)

(b)

(c)

(d)

(e)   State the domain of g.

(f)   State the range of g.

(3) A line has slope 9 and passes through the point (20, 4).   What is its x-intercept?
By the point-slope formula, the equation of the line is

Now, to find the x-intercept, set y = 0, and solve for x.

(4)

(5)

(6)

(7)

(8)

(9)

(10)   0

(11)

(12)    1

(13)   0

(14)  Consider the function .

Note (provided x is neither 0 nor -3 )

(a)    At which values of x is  f  discontinuous?

0 and -3 because f is not defined there

(b)
Find the vertical asymptotes (if any) of f.
The denominator is 0 for x = 0 or -3. These are the candidates for the locations of the vertical asymptotes.
, so no asymptote here.
, so line x=0 is a V.A.

(c)
Find the horizontal asymptotes (if any) of f.

, so line y = 1  is the horizontal asymptote.

(d) For which values of x does ?
We need to solve

Answer: x = 1