Time 1
Module 1 8:30
1. Find the derivatives of the following functions:
a). cos 3 (2 x 3) ;
sin x + 2 x
b).
.
x
2. Determine whether the following function:
if
2 x,
f ( x) = 2,
if
x 3 + 1, if
a). I
Time 2
Module 1 10:30
1. Find the limit (exactly):
lim
x 2
x + 4 3x
.
x 2 2x
In order to get the full credit for the exercise you must show all the work performed.
2. Calculate y: y =
1
.
sin( x sin x
Directions:
Please read the cover sheet carefully; you are responsible for the notices on the
sheet.
Show all your work. A correct answer without supporting work will not be
awarded any credit.
x 2
Module 1 Time 1 10:30 Fall 2007
Directions:
Please read the cover sheet carefully; you are responsible for the notices on the
sheet.
Show all your work. A correct answer without supporting work will
Problem 1. Since
f (x) =
we get
3
x x + 5 3 x = x5/6 + 5x1/3
5
1
5
5
f (x) = x1/6 + 5 x2/3 = x1/6 + x2/3 .
6
3
6
3
Also we have
g (x) =
1
sin(2x)
2
1/2
or
g (x) = sin(2x)
1
2 cos(2x) sin( x) x1/2
2
Show all of your work and explain your reasoning. A correct answer without supporting work will
not awarded credit.
1.
Find lim
x 0
5 x3 5
.
x3
Exit Exam Module 1 Time 2 10:30 Fall 2007
Show all of yo
Time 2
Module 1 12:30
1. Find the limits if they exist:
1
1
(2 + x ) 2
a). lim
x 0
x
b). lim
x
4
1 tan x
sin x cos x
In order to get the full credit for the exercise you must show all the work perform
CALCULUS 1 MATH 1411
SPRING 2008
Time 3
Module 1 12:30
1.
a.
b.
c.
d.
Determine whether the function is differentiable at x=2. Show your work.
f `(1)=
f `(3)=
f `(4)=
1
x + 1,
f ( x) = 2
2 x,
x<2
x2
CALCULUS 1 MATH 1411
SPRING 2008
Time 3
Module 1 10:30
x 2
x < 1
1. Let f ( x ) = x + 2
1 x < 3
1
3 x
x
a). Determine the interval(s) where the function is continuous (hints: sketch the graph
of the f
CALCULUS 1 MATH 1411
SPRING 2008
Time 3
Module 1 8:30
1) Find the limit:
2) Determine the value of
line.
such that the function is continuous on the entire real
IMPORTANT: In order to get the full cre
Show all of your work and explain your reasoning. A correct answer without supporting work will
not awarded credit.
1.
4 x
.
x 16 x 16
Find lim
Exit Exam Module 1 Time 2 8:30 Fall 2007
Show all of you
Time 2
Module 1 8:30
1. Calculate the following limits:
cos x x cos x
a. lim
h 1
2x 2 2x
1
1
2
2
( x + h)
x
b. lim
h 0
h
ax 2 + 1 x 2
2. Let f ( x) =
2 x 1 x > 2
a. Find the constant a so that the
Time 1
Module 1 12:30
1. Find the derivatives of the following functions:
a). f ( x) = 3 x sec( x) + sin( x 2 ) ;
b). g ( x) = x 2 3 .
2. State the intervals where the function is continuous:
x 2
x <
Directions:
Please read the cover sheet carefully; you are responsible for the notices on the
sheet.
Show all your work. A correct answer without supporting work will not be
awarded any credit.
1. Ca