M ATH 135 T HIRD M IDTERM E XAM
November 29, 2007
N AME :
S ECTION N UMBER :
1. Do not open this exam until you are told to begin.
2. This exam has 5 pages including this cover. There are 5 questions.
3. Do not separate the pages of the exam. If any pages
5.3-5.4: The Fundamental Theorem of Calculus
4-10-13
In the second stage of the Tour de Kazakhstan, cyclist Greg Legstrongs velocity (in
km/h)was described by the function
v (t) = 8t3 48t2 + 64t.
32
24
16
8
-1
0
-8
-16
-24
-32
1. Calculate
4
0
v (t) dt.
2
5.3: Evaluating Denite Integrals
Due: Beginning of class on Wednesday, April 10
4-8-13
1. 5.3: #3, 5, 7, 9, 11, 17, 29, 45, 47
2. I have a plate that has the shape of the region between the function y = x2 and the
x-axis from x = 1 to x = 5. At which poin
4.7: Antiderivatives
Due: Beginning of class on Wednesday, April 3
4-1-13
1. Find the derivatives of the following functions.
1
(a) 3x5 4x2 + x + x ln(x)
(b) x cos(x)
(c)
x2 1
x2 +1
2 1
(d) ex
(e) sin(cos(3x2 )
(f) sec(x) tan(x)
(g) sin2 (x) + cos2 (x)
(
Practice Problems
1. Let f (x) be the invertable function f (x) = (x + 2)ex and let g (x) = f 1 (x).
(a) Find g (2).
(b) Find g (2).
(c) If H (x) = (g (x) + 8)3 , nd H (2).
2. Compute the following limit:
1
lim+ (1 2x) x
x0
3. Compute the following integr
Practice Problems
1. Let f (x) be the invertable function f (x) = (x + 2)ex and let g (x) = f 1 (x).
(a) Find g (2).
By observation, since f (0) = 2, then g (2) = 0
(b) Find g (2).
From facts proved in class we know that:
1
f (g (x)
g (x) =
Since we know
M ATH 135 S ECOND M IDTERM E XAM
November 9, 2007
N AME :
S ECTION N UMBER :
1. Do not open this exam until you are told to begin.
2. This exam has 6 pages including this cover. There are 6 questions.
3. Do not separate the pages of the exam. If any pages
M ATH 135 S ECOND M IDTERM E XAM
November 9, 2007
N AME :
S ECTION N UMBER :
1. Do not open this exam until you are told to begin.
2. This exam has 6 pages including this cover. There are 6 questions.
3. Do not separate the pages of the exam. If any pages
M ATH 135 F IRST M IDTERM E XAM
October 16, 2007
N AME :
S ECTION N UMBER :
1. Do not open this exam until you are told to begin.
2. This exam has 6 pages including this cover. There are 6 questions.
3. Do not separate the pages of the exam. If any pages
M ATH 135 F IRST M IDTERM E XAM
October 16, 2007
N AME :
S ECTION N UMBER :
1. Do not open this exam until you are told to begin.
2. This exam has 6 pages including this cover. There are 6 questions.
3. Do not separate the pages of the exam. If any pages
M ATH 135 T HIRD M IDTERM E XAM
November 29, 2007
N AME :
S ECTION N UMBER :
1. Do not open this exam until you are told to begin.
2. This exam has 5 pages including this cover. There are 5 questions.
3. Do not separate the pages of the exam. If any pages
5.5: The Substitution Rule
Due: Beginning of class on Wednesday, April 17
Use u-substitution to evaluate the following integrals:
2
1.
2xex dx =
2.
8x
14x2
3.
x2 sin(x3 ) dx =
4.
sin(x) cos(cos(x) dx =
5.
6.
31
0 5x+1
dx =
dx =
x x 1 dx =
4-15-13
7.
cos4