Ethan Atwood
Reading 11.2
Summary: Numbers such as pie can be written as an infinite series or a summation that
approximate pie. These summations are considered convergent if they exist as the limit
as n goes to infinity, and divergent if they do not exis
Than. 2 Math 112 March 8, 2005
NAME 9:20. 10:20, [2:20
Circle your class time.
0 PLEASE NOTE: You may use the table of integnls provided wherever It. applies. You must
state the number of the formula that you are using as well as values for each symbol us
April 19, 2304
Math 112 Practice Ebcam III
Show all work clan-bx; an answer with no justin'ng computh may not zeaeive credit (except
for the write down but do not evalmté qustions).
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Test 1 Math 112 February 8. 2005
NAME, 9:20. 10:20. [2:20
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o No calculator is allowed. Do not. round off nmwers. If you get 10/6 as an answer, you should
leave your anew as 5/3. No decimal approximations, please.
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Math 112 Practice Exam [I
Show 111 work clearly; an m with no justifying oompth any noi naive credit. (map:
for the write dawn but, do not walnut! questions). If my divers-5m Improper integrals appear,
state that they are divergent.
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March 10, 2004
Math 112 Exam II
Show all work clearly; an answer with no justifying computations may not receive credit (except
for the write down but do not evaluate questions). If any divergent improper integrals appear,
state that they are divergent.
1
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(b) lim hastheindenite forml"°. Lety= (53)'.solny=xh(*;~2). Then
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February 18, 2004
Math 112 Exam I
Show all work clearly; an answer with no justifying computations may not receive credit (except
in the set up but do not evaluate problems).
1. (15 points) (a) Find the equation of the tangent line to the graph of $2 + Qx
Final Exam Math ll? December 14, 2006
NAME
0 No calculator is allowed. Do not round off answers. If you get 10/6 as an answer, you should
leave your answer as 5/3. No decimal approximations. please.
0 For problems with numerical approximation of integrals
May 6. W
Math 112 Final Exam 8
Show All work clearly; an m with no justifying mmpmalm may not receive wait (except
for me mm-down but do not evaluate (amnion).
l. (somuziaduimd Ioappmximalothe lengthoho parametric cum: = £~t,y = 2
for 2 $158.
(a) Write ou
Fain-um 1?, 3304
Math 119 Practice Etam I
Show all work clarly; an answer with no justidng computations may not receive credit- (except
in the set up but do not evaluate"
1. (159001728) (.1) Find the eqwimof the two tangem linsto thegmph date-+3? = (223+
Ethan Atwood
9.1 Modeling with Differential Equations
Summary: A differential equation is an equation that includes an unknown function and
its derivatives. Differential equations can be used to model population growth as dP/dt
where t is time and P is th
Ethan Atwood
Reading 11.9
Summary: Certain functions can be represented as sums of power series. This is done
through manipulating geometric series or differentiating/integrating geometric series.
However the differentiating/integrating is one term by ter
Ethan Atwood
HW 9
Reading 7.2
Summary: Section 7.2 is about trigonometric integrals. When taking the integral of a
trigonometric function to a given power, simple u substitution can be insufficient.
However breaking up the trigonometric function and subst
Ethan Atwood
Reading 7.2 Continued HW 10
A similar strategy can be used to evaluate integrals of tan and sec x to the m power.
Solving these integrals may require integration by parts, identities, or even simple u
substitution.
Strategy for Evaluating int
Ethan Atwood
7.4 Reading
HW 11
Summary: Integration of Rational Functions by Partial Fractions is the topic. Partial
fractions are useful because they make complex equations easier to deal with. In f(x) =
P(x)/Q(x) p can be divided by q in order to obtain
Ethan Atwood
7.5 Reading
Summary: Since integration is far more complex than differentiation, many integrals have
abstract formulas. Memorizing basic integration formulas can solve many integrals.
However there are also steps to solve integrals when the m
Ethan Atwood
8.1 Reading
Summary: the length of a curve is equivalent to the length of a piece of string fitted to
that curve. Given a Riemann sum approximation, an arce length formula can be derived.
Arc length formula:
if f prime is continuous on [a,b],
Ethan Atwood
Reading 7.7
HW 16
Summary: Sometimes it is impossible to find the exact value of a definite integral
because integrating f(x) is not plausible. Either f(x) is a function that cannot be
integrated, or f(x) is based on a data set not a specific
Ethan Atwood
Reading 4.4 Continued
Summary: A limit of indeterminate products results when the lim from x to a of f(x) is 0
while that of g(x) is +/- infinity. If we write the product of fg as a quotient the
indeterminate form becomes doable. A limit of i
Ethan Atwood
9.3 Separable Equations
Summary: A separable equation is a first order differential equation with dy/dx can be
factored x(y) times. Rather dy/dx = g(x)f(y). To solve separable equations, f(y) = 1/h(y)
so that h(y)dy = g(x) dx. Both sides of t
Ethan Atwood
Reading 9.5
Summary: Linear equations are often used for scientific purposes. Given continuous
functions p(x) and q(x), a first order linear differential equation takes the form dy/dx +
p(x)y = q(x). These equations are not separable. Yet in
Ethan Atwood
11.3: The Integral Test and estimates of Sums
Summary: Series that approximate sums can be evaluated to determine convergence or
divergence without actually discovering the value of the series. The integral test can be
used to o this. Given c
Ethan Atwood
Reading 11.8
Summary: 11.8 is on power series. In a power series, a variable x is raised to the nth
power and is sometimes multiplied by constant c_n. A power series is equivalent to a
polynomial with an infinite number of terms. The sum is e
May 3. W
Math 112 Final Exam A
Show All work clearly; an m with no justifying amputations may not receive wait (except
for the "wxltedown but do not evaluate (nautical).
l. (somnutbduiredtonpptoximuetbelengthofthecumy=z+forlgzsz
(11) Write out, but do not