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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