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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

Answer: x = 1