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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