Class Ib:
Name:
OkiOr’S
MATH 1210-008
Midterm 1
U____________
FaIl 2012
September 20, 2012
SHOW ALL WORK. As partial credit will be given where appropriate, arid there
may be NO credit given for answers without supporting work.
o Scratch paper will be provided by the instructor, just ask. Scratch work will not
o
o
o
o
o
o
be graded, record all work that is part of your solution on this exam.
Make sure your work is organized and legible.
Answers should be simplified, unless otherwise indicated
Box or Circle your final answers.
NO CALCULATORS, NOTES, PHONES, ETC.
You may use a 3x5 index card for reference.
bo NOT write in the table.
Prob. Score
1
/20
2
/7
3
/7
4
/15
/15
5
/30
6
/6
7
Total
/100
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2. Use calculus to find the horizontal asymptote of g(x)
=
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-3
.rf’
-3
—
—
.
ci
-
‘
—
—
The horizontal asymptote of
g(x)
is y
3. Use the limit definition of the derivative to find the f(x) when
f(x) =gx+2
.
-
-
)C
.
—
)
D/x+2=
°
.
=________
4. a) What 3 conditions must be met so that a function is continuous at xc?
(Hint: These 3 condition are the definition of a continuous function at xc)
a)
I
a
S
.
rr)
s 4c) cc’)
b) Sketch the graph of a function so that f(c) is undefined but limf(x)
Is this function continuous?
YES
=
(circle one)
or
I
c) Sketch the graph of a function so that f(c)
exist.
Is this function continuous?
YES
d) Sketch the graph of a function f(c)
Is this function continuous?
YES
=
—2 but Iimf(x) does not
or
=
5 but limf(x)
or
(circle one)
=
—1,
(circle one)
5. Calculate the following derivatives.
—
6
y=5x
—
2
f
1
4÷x
ind
x y’.
a) 3
y=
3Q-2%-
3
b) Assume that the function, f, has a derivative for all real numbers.
D [—7f(x)j
-1
D[-7f(x)j
d.
dx
c) —(sinx--cosx)
d.
dx
—(sinx —cosx)
d) Show that D(secx) =secxtanx.
C oSL
(-)(Cos)
cosi
)
=
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C)
C’
—
4.
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7. Find the tangent line of f(x)
=
3sin(2x) + 4 at x
=
0.
(o,L4
cc
(i)
••
-
t
—\
DCOS.%)
oscp’
c;)
The tangent line of f(x) when xO is