Transcript Calcpardy Double Jep AB 2010

The equation of the tangent to the
curve 2x2 - y4 = 1 at the point
(1,1) is this.
What is y=x?
5
lim
x 2 x  2
is this.
What is infinity?
1
is
this.
dx
 x ln x
1
2
What is (ln x)  C+ C
2
sin(2x)
cos
(2x)dx
is
also
this
function.

2
What is
1
3
 cos (2x)  C ?
6
If f(x) is continuous,f(1) = 8
and f(4) = -3, this theorem
tells me that f(x) must pass the
x-axis at least once between
x=1 and x=4.
What is the Intermediate Value
Theorem?
The Mean Value Theorem tells us
that if a function is differentiable on
an interval then there is a value in
that interval at which the slope of the
tangent line is equal to this quantity.
What is the average rate of change on
the interval?
Or
What is the slope of the secant line?
The derivative of y = ln(u) with
respect to x is this.
What is
1 du

u dx
?
This graph can assist in
visualizing the solution to a
differential equation.
What is a slope field?
3x  2x  x  1
y
2
5
5  2x  3x
4
2
has a horizontal asymptote at this
line.
What is y=0?
These are values where the
derivative of a function is zero or
undefined.
What are critical points?
This ancient mathematical cult
hid the existence of irrational
numbers fearing their impact on
mathematics.
Who are the Pythagorians?
This mathematician is most well
known for the theorem stating
n
n
n
that a  b  c has no integer
solutions for a, b, and c when n is
a natural number greater than 2.
Who is Fermat?
This famous mathematician /
computer scientist was submitted
to experiments using drugs
because of his sexual preference.
Who is Alan Turing?
This French mathematician died
in a duel at the age of
20…leaving behind a legacy of
hastily scribbled theorems.
Who is Evariste Galois?
This is the full name of the
English mathematician who cocreated the study of Calculus.
Who is Sir Isaac Newton?
d
 log a u 
dx
is this.
1
du
What is
?
(ln a)(u) dx
2
x
The area between y = and y=x
is this number.
What is 1/6?
3x  2
dx
 x 3  2x  6
gives this family of functions.
2
What is ln x  2x  6  C ?
3
The slope of the tangent line to the
curve given by
xy2 + 2xy + 3x = 4 when x = 2 is
this.
What is undefined?
The area between the graphs of
cosx and sinx between two
consecutive intersection points.
What is
2 2
?
2
sin (4θ)
+
2
cos (4θ)
is always this
number.
What is One?
As long as b≠0, then if
logba=0, a must be this
number.
What is 1?
The limit of (sin x)/x as x
approaches zero.
What is one?
The area between x=0
and x=π bounded by the
x-axis and the sine
function.
What is 1 +1?
Song by Bob Marley
whose title might have
been a better name for this
category.
What is “One Love”?
DAILY
DOUBLE
DAILY
DOUBLE
FINAL
JEOPARDY
CALCPARDY
Theorems
Applied
Pot-Pourri
Mathematicians
Problem
Solving
The Loneliest
Number
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F
The formula for the surface
area of a sphere
If f(x) is continuous,f(1) = 8
and f(4) = -3, this theorem
tells me that f(x) must pass the
x-axis at least once between
x=1 and x=4.
What is the Intermediate Value
Theorem?