Test time = 8:30 11:30 (+5 points, if you circle the correct one) MAT 200 Fall 2006, Exam 1, Sept 26, Style (Maximum of +5 points) Name (+5 points if your name is printed legibly)
1. (+10 points) The speed of a roller coaster is measured at 1-minute
TEST 2
(MATH 200 (A), Fall 06)
1. Evaluate the following integral:
2 sin 6 cos 2 d .
(10 pts)
2. Show that:
/4
0
tan 4 x sec 4 x dx
12 . 35
(10 pts)
3. Using the identity cos 2 x sin 2 x cos 2 x , show that:
(Hint: This should take yo
TEST 2
(MATH 200 (A), Fall 06)
1. Evaluate the following integxal: g2 sin 66 cos 26 d0 . ' (l0 pts)
f" q . . l» , f V . _b
r 5 f ,. ~ 4; "~ 2 ; n 5 ~' r x i g an) r;
{3 a. mainlmoéliSgnnmgdy293; 0:9 ~: 4a,; *_,~»f
X y p L; 2H3»- w j r \ axe A
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Midterm Exam
(Math 200 A, Fall 06)
Solve the following problems. Show all your work in the space under each problem.
1. Answer the following: (a) Evaluate the integral:
(15 pts)
2
1
1 (1 ) dx x
(b) The result you found in (a) describes: A.
HOMEWORK 2
(Math 200 A, B)
1. What is the value of c if
(1 c)
n2
n
2 ?
(10 pts) (30 pts)
2. The Fibonacci Sequence is defined by the following equations: f 1 1 , f 2 1 , f n f n 1 f n 2 , where n 3 . Show the following: (a)
1 1 1 f n
HOMEWORK 1
(Math 200 A, B)
1. Establish the following reduction formulas: (a) sec n x dx
n
(20 pts)
sec n 2 x tan x n 2 sec n 2 x dx n 1 n 1
tan n 1 x tan n 2 x dx (b) tan x dx n 1
(Hint: Write sec n x as sec n 2 x sec 2 x and make use
TEST 3
(MATH 200 (A), Fall 06)
1. Use partial fractions to show that
k (k 1) 1 .
k 1
1
(10 pts)
2. For the geometric series (a) the first three terms
e
n 0
3 n
, find the following: (b) The ratio r
(15 pts) (c) The sum of the series.