Math 124D, Summer 2012
Quiz 0: Solutions
Page 1 of 1
1. Decompose the function
h(x) =
cos(x)
into simpler functions. More specically, write h as
h(x) = f (g(x)
and explicitly indentifty the functions f and g.
Let f (x) =
x and g(x) = cos(x). Then
f (g(x)
Math 124D, Summer 2012
Final Exam
Your Name
University of Washington
Student ID #
This exam is closed books. This exam is closed book. You may use one 8.5 11 sheet of
handwritten notes (both sides OK).
Do not share notes. No photocopied materials are all
Math 124D, Summer 2012
Midterm 1
Page 1 of 4
1. (6 total points) Determine the following limits. If the limit is not nite, determine whether the limit
tends to +, , or does not exist.
t 1
(a) (2 points) lim 2
t 1 t 1
t 1
t 1
1
1
= lim
= lim
=.
21
t 1 t
t
Math 124D, Summer 2012
Midterm 1
Your Name
University of Washington
Student ID #
This exam is closed books. This exam is closed book. You may use one 8.5 11 sheet of
handwritten notes (both sides OK).
Do not share notes. No photocopied materials are allo
Math 124D, Summer 2012
Quiz 5: Solutions
Page 1 of 1
1. Consider the equation below.
f (x) = 2x3 + 3x2 72x
(a) Find the intervals on which f is increasing and decreasing, respectively.
The derivative is
f (x) = 6x2 + 6x 72 = 6(x2 + x 12)
By the quadratic
Math 124D, Summer 2012
Midterm 2: Solutions
Page 1 of 4
1. (6 total points) Differentiate the given function.
cos(x)
(a) (2 points) y =
x
By the quotient rule,
d cos(x)
=
dx
x
1
d
d
x dx cos(x) cos(x) dx x x sin(x) cos(x) 2x
x sin(x) 1 cos(x)
2
2
.
=
=
3
Math 124D, Summer 2012
Quiz 3: Solutions
1. Differentiate the function
Since
2
1
x+
4
x
1
x+
4
x
1
1
= x 2 + x 4
Page 1 of 1
2
.
2
1
1
= x + 2x 4 + x 2 ,
it follows that
1
d
x+
4
dx
x
2
=
1
1
1313
d
x + 2x 4 + x 2 = 1 + x 4 x 2 .
dx
2
2
2. Suppose that
Math 124D, Summer 2012
Quiz 4: Solutions
Page 1 of 1
1. Differentiate the function
cos(1 + x9 ).
d
d
cos(1 + x9 ) = sin(1 + x9 ) x9 = 9x8 sin(1 + x9 ).
dx
dx
2. Find an equation of the tangent to the curve at the point corresponding to the given value of
Math 124D, Summer 2012
Quiz 2: Solutions
Page 1 of 2
1. Use the given graph of f to state the value of each quantity, if it exists. (If an answer does not exist,
write DNE).
2
1
0
-1
0
1
2
3
4
5
-1
-2
(a) limx2 f (x)
The graph approaches the value
1
2
1
f
Math 124D, Summer 2012
Quiz 1: Solutions
Your Name
Page 1 of 2
Student ID #
A scientic calculator is allowed, but graphing calculators are not allowed.
In order to receive full credit, you must show all of your work. If you do not indicate the way in
wh
Math 124D, Summer 2012
Midterm 2
Your Name
University of Washington
Student ID #
This exam is closed books. This exam is closed book. You may use one 8.5 11 sheet of
handwritten notes (both sides OK).
Do not share notes. No photocopied materials are allo
Math 124D, Summer 2012
Final Exam: Solutions
Page 1 of 6
1. (10 total points) Consider the function
ex
.
x
(a) (3 points) Determine the domain of f , and check for vertical and horizontal asymptotes. In view
of part (d), check both one-sided limits for th