MATH 1585H CRN 41953
Honors Calculus: Quiz 5
Name :
Fall 2011
Score :
tan x 1
x/4 x /4
1. Calculate the limit: lim
2. Using the denition of the limit, prove that lim x2 = 1 .
x1
/10
MATH 1585H CRN 41953
Name :
Honors Calculus: Exam 4-More Integration
Fall 2011
Score :
/108
This exam includes 18 questions. Each problem is worth 6 points. Note that there are 8 extra bonus points
built into this exam. Please show all work. Good Luck!
1.
MATH 1585H CRN 41953
Honors Calculus: Quiz 1
Name :
Fall 2011
Score :
/10
1. Sketch the graph of a function that satises
(a)
lim g (x) = 1
lim g (x) = 1,
x2
(b) lim g (x) = 0,
x2
x2+
lim g (x) = 1
x2+
(c) g (2) = 1, g (0) undened
2. Determine the followin
MATH 1585H CRN 41953
Name :
Honors Calculus: Exam 4
Fall 2011
Score :
/108
Each problem is worth 7 points. Note that there are 8 extra bonus points built into this exam. Please
show all work. Good Luck!
1.
x2
x
dx
+4
2cos x sin x dx
2.
3.
(tan5 x sec3 x)
MATH 1585H CRN 41953
Name :
Honors Calculus: Exam 3
Fall 2011
Score :
/110
This exam includes 12 questions. The total number of points is 110. Note that there are 10 extra bonus
points built into this exam. Please show all work. Good Luck!
1. (5 points) F
MATH 1585H CRN 41953
Honors Calculus: Exam 2
Name :
Fall 2011
Score :
/110
Note that there are 10 extra bonus points built into this exam. Please show all work. Good Luck! Some
formulas that you may nd helpful: The volume of a cone is given by V = 1 r2 h,
MATH 1585H CRN 41953
Name :
Honors Calculus: Exam 2(a)
Fall 2011
Score :
/105
Note that there are 5 extra bonus points built into this exam. Please show all work. Good Luck! Some
formulas that you may nd helpful: The volume of a cone is given by V = 1 r2
MATH 1585H CRN 41953
Honors Calculus: Quiz 2
Name :
Fall 2011
Score :
/10
1. Help me ll in the following gaps in the proof that lim (2x + 2) = 8 using the denition.
x3
Here L =
,a =
, and f (x) =
.
Let > 0.
Show: There exists > 0 such that if 0 < |x a| <
MATH 1585H CRN 41953
Honors Calculus: Quiz 3
Name :
Score :
(
1. Using the denition of the limit, prove that lim
x1
)
x
1
+1 = .
2
2
2. Determine the innite limit:
lim cot x.
x
cfw_
3. Let
f (x) =
1 x2 if x < 1
1
if x 1
x
4. (a) Using the denition of con
MATH 1585H CRN 41953
Name :
Honors Calculus: Quiz 8
Fall 2011
Score :
/10
1. A man launches his boat from point A on a bank of a straight river, 5km wide, and wants to reach a
point B , 5km downstream on the opposite bank, as quickly as possible. He could
MATH 1585H CRN 41953
Honors Calculus: Quiz 9
Name :
Fall 2011
Score :
/10
1. Calculate the following limit by rst recognizing it as a Riemann Sum, and then evaluating a denite
)
n
(
3i 2 3
integral: lim
2+
n
n
n
i=1
2. Find the derivative of y =
1
13x
3.
MATH 1585H CRN 41953
Honors Calculus: Quiz 7
Name :
Fall 2011
Score :
1. Calculate the following limits. Be sure to show all of your work.
(
)
1
1
(a) lim
x 0 x 1 + x
x
2x2 x
x0 sin x
(b) lim
2. The position of a particle is given by the equation
s = f (t
MATH 1585H CRN 41953
Honors Calculus: Quiz 6
Name :
Fall 2011
Score :
1. Calculate the following limits. Be sure to show all of your work.
sin(2x)
(a) lim
x0 tan(4x)
(b) lim
x0
cos x 1
x
2. Show that
d
cos x = sin x using the limit denition of the derivat
MATH 1585H CRN 41953
Honors Calculus: Quiz 4
Name :
Fall 2011
Score :
1. Using the denition of the limit, prove that lim x2 = 0 .
x0
2. Show that there is a root of the equation 4x3 6x2 + 3x 2 = 0 between 1 and 2.
3. Calculate f (a) using the denition of
MATH 1585H CRN 41953
Name :
Honors Calculus: Exam 1
Fall 2011
Score :
/110
Note that there are 10 extra bonus points built into this exam. Please show all work. Good Luck!
1. (15 points) Find the derivative of each of the following functions. SHOW YOUR WO