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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 .

From sec(θ)=8, we get , or .
Also, , meaning
Then =.  But, as is in the first quadrant, is the POSITIVE square root of 63.

(d)   Find all solutions of the equation

Looking at the unit circle, you can see that the solutions are all values of x of the form
or     , where n is an integer.

(2) Suppose     and   .

(a)   sin()+1 = 1

(b)

(c)

(d)

(e)   State the domain of f.   All real numbers.

(f)   State the range of f.    [0, 1]

(3) Find the equation of the line having slope and passing through (4, 5). Put your answer in slope-intercept form.

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(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