Improper Integrals
Comparison Theorem
Arc Length
Surface Area
Sequences & Series
Tim's Trivia
100
\int _0^infty sin x dx
DNE
100
To show
\int _4^infty f(x) dx
diverges, find a similar function
g(x)>0
with
_____ < ______ and where
\int _4^infty g(x) dx
_________.
g(x)<f(x)
diverges
100
Set up but do not evaluate an integral with respect to x which represents the length given that
y=x^3
between (1,1) and (2,8).
\int _1^2 \sqrt{1+(3x^2)^2} dx
100
Write the general form of the surface area formula for a function in terms of x rotated around the y-axis.
\int _a^b 2pix\sqrt{1+(f'(x))^2} dx
100
How do we know if a series diverges?
lim _{n->infty} a_n ne 0
100
What's the capital of North Dakota?
Bismarck
200
\int _0^infty \frac{1}{1+x^2}dx
\frac{pi}{2}
200
To show
\int _4^infty f(x) dx
converges, find a similar function
g(x)>0
with
_____ < ______ and where
\int _4^infty g(x) dx
_________.
f(x)<g(x)
converges
200
Set up but do not evaluate an integral which represents the length with respect to y given that
y=x^3
between (1,1) and (2,8).
\int _1^8 \sqrt{1+(\frac{1}{3}y^{\frac{-2}{3}})^2} dy
200
Set up an integral for
y=sin(pix)
from (0,0) to (1,0)
\int _0^1 2pi sin(pix)\sqrt{1+(pi cos(pix))^2} dx
200
Write the first 5 terms of the following sequence.
a_n = \frac{2^n}{n!}
2, 2, \frac{4}{3}, \frac{2}{3}, \frac{4}{15}
200
Name that flag.
Romania or Chad
300
\int _0^infty e^\frac{-x}{2}dx
2
300
Use Comparison Theorem to determine whether each integral converges or diverges.
\int _1^infty \frac{x}{\sqrt(2+x^6} dx
converges
300
Set up an integral with respect to x which represents the length
y=e^x
between the points
(0,1), (2,e^2)
\int _0^2 \sqrt{1+(e^x)^2} dx
300
Set up an integral for the surface area by rotating
y=sqrt{9-x^2}, -3 leq x leq 3
around the x-axis.
\int _-3^3 2pi sqrt{9-x^2}\sqrt{1+(\frac{-x}{sqrt{9-x^2}})^2} dx
300
Determine if the following series is arithmetic or geometric. Justify if the series is convergent or divergent.
sum _{n=0}^infty [(\frac{2}{3})^n - \frac{1}{5^n}]
Geometric
\frac{7}{4}
300
Who was the second person to sign the Declaration of Independence?
Josiah Bartlett
400
\int _0^\frac{pi}{2} tan x dx
Diverges
400
Use Comparison Theorem to determine whether each integral converges or diverges.
\int _1^infty \frac{sin(x)+3}{\sqrt x} dx
diverges
400
Set up an integral with respect to y which represents the length
y=e^x
between the points
(0,1), (2,e^2)
\int _1^{e^2} \sqrt{1+(\frac{1}{y^2})^2} dy
400
Set up an integral and compute the surface area by rotating
y=sqrt{4-x^2}, -1 leq x leq 1
around the x-axis.
8pi
400
Justify whether the Divergence Test can be applied to the following series.
sum _{n=2}^infty \frac{ln(3n)+1}{3n}
We cannot justify using the divergence test.
400
Name the movie this quote comes from and the character who says it.
“Lembas Bread, one bite is enough to fill the stomach of a full grown man.”
The Lord of the Rings; Legolas
500
\int _0^1 ln x dx
-1
500
Use Comparison Theorem to determine whether each integral converges or diverges.
\int _0^infty e^{-x}sin^2(x)dx
converges
500
Find the length of the curve
y=ln(cos(x)), 0 leq x leq \frac{pi}{3}
ln|2+sqrt{3}|
500
Find the area of the surface obtained by rotating
y^2 = 4x+4, 0 leq y leq 2
about the x-axis.
\frac{16sqrt{2}pi}{3}-\frac{8pi}{3}
500
Determine if the following sequence is bounded above/below, both, or neither; increasing/decreasing or neither; and convergent or divergent.
a_n = 2-(-1)^n
bounded; neither increasing or decreasing; divergent
500
What is the name of the period element that has the symbol Yb?
Ytterbium