Calculus Jeopardy

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Calculus Jeopardy!
Calc II the sequel

• Produced by the USF Mathematics Program
• Hosted by the ever-affable Jason Douma

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This semesters categories

• Formula Fun
• Seriesous Business
• Graphically Speaking
• Integrate This!
• Call the Terminologist
• Is this stuff actually useful?

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Formula Fun 100 is the formula
for what?

• This formula will give the area of the sector
  from the origin out to the polar curve r f(?)
  as ? ranges from a to ß.

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Formula Fun 200 In the formula
the radical in the integrand represents this
physical quantity.

• The length of the hypotenuse of a very small
  right triangle (with the dx factored out).
• (This is our arc length formula.)

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Formula Fun 300 The formula
gives us what?

• The Taylor series for the function f(x) centered
  at x a.

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Formula Fun 400 This is what the
represents in the moment formula .

• This is the y-coordinate of the center of an
  infinitesimally thin rectangle within the region
  being evaluated.

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Formula Fun 500 This is the formula for
the integrating factor in a first-order linear
differential equation .
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Seriesous Business 100 This is an example
of a conditionally convergent series.

• Answers may vary, but is a
  good example.

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Seriesous Business 200 This convergence
test is especially useful for series that have
factorials in their terms.

• The ratio test.

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Seriesous Business 300 This is an example
of a series whose terms converge to zero, but
whose partial sums do not converge at all.

• Pick from any number of divergent series whose
  terms approach zero. The harmonic series is a
  classic example.

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Seriesous Business 400This is what the
series converges to.

• 6

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Seriesous Business 500 This is the
Maclaurin series for .

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Graphically Speaking 100This is what the
graph of the polar curve r 3 looks like.

• Its a circle of radius 3 centered at the origin.

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Graphically Speaking 200 The solution
curves to the differential equation
have this shape.

• They are shaped like exponential curves.

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Graphically Speaking 300 For what value(s)
of ? do the polar curves and
intersect?
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Graphically Speaking 400 Of the ellipses
and
this is
the ellipse with the larger eccentricity.
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Graphically Speaking 500 These is the
location of the focus of the parabola
.

• (0,5)

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Integrate This! 100

• sin-1 x C

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Integrate This! 200 These are the most
appropriate choices for u and dv if using
integration by parts to evaluate the integral
.
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Integrate This! 300 This is the
integration technique which is most likely to be
effective in evaluating the integral .

• Trigonometric substitution.

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Integrate This! 400 This is the solution
to the initial value problem , with
.
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Integrate This! 500

• 1

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Call the Terminologist 100What is a
p-series, and for which values of p does a
p-series converge?

• A p-series has the form for some
  constant p. It converges if pgt1.

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Call the Terminologist 200 Fill in the
blanks with proper choices from the following
list geometric, power, harmonic, Taylor,
and MaclaurinA __________ series is a
special case of a __________ series, which is
itself a special case of a ___________ series.
Maclaurin, Taylor, power
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Call the Terminologist 300 A general
solution to a differential equation consists of
this.
The collection of all functions that satisfy the
differential equation (hence the arbitrary
constant(s)).
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Call the Terminologist 400 This type of
conic section has a general form equation with a
positive discriminant.

• Hyperbola

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Call the Terminologist 500 This is what
makes an improper integral.

• The integrand is undefined at , which
  lies in the middle of the interval of integration.

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Is this stuff actually useful? 100Set up
(but do not evaluate) the integral that would
give us the volume of the solid of revolution
obtained by revolving around the
x-axis over the interval 1,4.
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Is this stuff actually useful? 200If a
population of grouse is properly modeled by the
differential equation
, and if the current population of grouse is
50, then is the population currently increasing,
decreasing, or stable?

• Decreasing

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Is this stuff actually useful? 300Set up
(but do not evaluate) the integral that would
give us the surface area of the solid of
revolution obtained by revolving
around the x-axis over the interval 1,4.
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Is this stuff actually useful? 400Find the
volume of the torus generated by revolving a
circle of radius 2, centered at (6,0), about the
y-axis.

• (Hint Use Pappuss theorem.)

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Is this stuff actually useful? 500Given a
spring whose force constant is k 8 lb/ft, find
the work required to stretch the spring 3 feet
beyond its resting position.

• 36 ft-lbs.

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Final Jeopardy!

• Category
• If you were stranded on a deserted island without
  a calculator
• Question
• How many terms from the Maclaurin series for sin
  x would you need to add in order to estimate
  sin(.1) to within .0001 of its true value?
  
• Answer
• 2 terms (i.e., the 3rd degree Taylor polynomial)