Math 30 - Spring 11
Final Exam
Name:
Problem 1.
Find the domains of the following functions: (a) f (x) =
6 e3x . (b) g(x) = ln(1 ln 7x).
Solution:
Problem 2.
Solution:
Find the limit (innite or otherwise, if it exists): lim
t9
9t
.
3 t
Problem 3.
Evaluat
Math 30 8805 - Fall ’15 Test 3
Name:
dzv
d
Problem 2. Find T (sinmf‘m.
c :2:
Solution:
mszmm Problem 3. (Two parts) A particle moves along the :zr—axis with position
given by : t—l— sint. (a) During the time interval from t 2 0 to t = 27?,
when i
Math 30 Sec 3 - Fall ’15 Test 2
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£ M
Name: ®i%2a§ﬁg
1
Problem 1. Find the domain of (f o Where = E, and
$+1
a:—-1'
gm =
Solution:
Problem 2. Show that there is at least one root of the equation cos x~a3 = O
in the interval (0, 1).
Solutlon:
{
Math 30 Sec 3 — Fall ’15 Test/Quiz 1
m t: x- ,
a: 5:; may: at
t %
Name:
i i o 3' i .‘ x" t , v 3
(b) 9(33) ._ 1 from»), {Mao} {M :x; W“ ~'
._ . R > k. y» x”. ; mam: i s a»
1 + + 1 I f M a ‘ it " ‘ i I V l a a \ i ‘_ I, W fﬂ
Solutions:
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N": l. 4‘ ’“
Math 30 - Spring 11 Final Exam
(’9‘ _ i ‘
Name: «3? i‘. iﬂ‘": ﬁgﬁé
Problem 1. Find the domains of the following functions: (a) f 2
V 6 — 6393. (b) 9(33) 2 ln(1 -— ln 7w).
Solution:
CL} C” on
£133 6 a ,2
Problem 2. Find the limit (inﬁnite or otherwise, i
Math 30(6) - Spring 12
Test 3
Name:
Problem 1.
1
Find the derivative of y = esin
(x2 )
.
Solution:
Problem 2.
Suppose quantities x, y satisfy
dy
by implicit dierentiation.
derivative
dx
Solution:
3
xy = 2 + y 2 . Find the
Problem 3.
2
Find y given that y
Math 30 - Spring 11
Test 2
Name:
Problem 1.
Evaluate the limit, if it exists: lim
t0
1
1
. If the
t 1+t t
limit does not exist, explain why not.
Solution:
1
1
lim
t0 t 1 + t
t
1 1+t
= lim
t0
t 1+t
1 1+t
1+ 1+t
= lim
t0
t 1+t
1+ 1+t
1 (1 + t)
= lim
t0 t
Math 30(6) - Spring 12 Test 3
Name: Wm 9
Problem 1. Find the derivative of y :2 esmhlcﬂg).
if «a
m » . r t
K x N‘ J r if,
i r Vt i 3x I, ”
Solution:
Problem 2. Suppose quantities 9:,y satisfy 9/31] 2 2 + 3/2. Find the
dy
derivative 2Z— by implic
Math 30 - Spring 11
Test 1
Name:
Problem 1.
Find the domain of the function: f (x) =
x
.
x2 9
Solution:
Problem 2. Let f (x) = 2x5 4x2 + 2. Is f even, odd, or neither? Justify
your answer algebraically, using the denition of even and odd functions.
Soluti
Math 30 - Spring 11
Test 1
Name:
Problem 1.
Find the domain of the function: f (x) =
x
.
x2 9
Solution:
To be in the domain of f , x must be 0 (and so in the domain of x), and
at the same time not equal to 3 (so that the denominator = 0). In other
words,
Math 30 - Spring 11
Test 2
Name:
Problem 1.
Evaluate the limit, if it exists: lim
t0
1
1
. If the
t 1+t t
limit does not exist, explain why not.
Solution:
Problem 2. Evaluate the limit using continuity: lim e2x (x2 + 9). Explain
x0
why this method applies
U-boats Devastating Effect on the Great War
Rediet b. Bekele
U.S history 17B
Professor Carrie Prater
April 08, 2014
Usage of U-boats
Bekele 2
Aside from the human involvement in the Great War, which was very unpredictable
and infinitely variable in all, p