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
a
Than. 2 Math 112 March 8, 2005
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April 19, 2304
Math 112 Practice Ebcam III
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Test 1 Math 112 February 8. 2005
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March 10, 2004
Math 112 Exam II
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for the write down but do not evaluate questions). If any divergent impr
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February 18, 2004
Math 112 Exam I
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in the set up but do not evaluate problems).
1. (15 points) (a) Find t
Final Exam Math ll? December 14, 2006
NAME
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leave your answer as 5/3. No decimal approximations. please.
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May 6. W
Math 112 Final Exam 8
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for me mm-down but do not evaluate (amnion).
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Math 119 Practice Etam I
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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
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.
How
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.
H
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
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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(
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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.
How
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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.
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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
in
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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 quoti
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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,
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
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 s
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
po
May 3. W
Math 112 Final Exam A
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for the "wxltedown but do not evaluate (nautical).
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