Math 231 Worksheet #23 Solutions
1. Which is larger, 3
or 34 ?
4
Solution:
3
(3)(3 1)(3 2)(3 3)
3456
=
=
= 15
4!
4!
4
3
3(3 1)(3 2)(3 3)
=
=0
4
4!
P

n
2. If limn ccn+1
=
3,
then
what
is
the
rad
Math 231 Worksheet #18 Solutions
1. (Ratio test and Radius of convergence.)
P
an+1
n
(a) Consider a power series
a
x
.
Suppose
that
lim
n an = L. What is
n=0 n
the radius of convergence of the powe
ECE 391 MP1 Grade Sheet
Comments (10)
Full Interface for each function
Commenting within function bodies
_/5
_/5
Compilation (10)
No errors/warnings in userlevel test harness compilation
No errors/wa
Math 231 Worksheet #24 Solution
1. Consider the following.
x = et ,
y =t+3
Eliminate the parameter to find a Cartesian equation of the curve. Then sketch the
curve and indicate with an arrow the direc
Math 231 Worksheet #21 Solutions
1. You have a mystery function f . You know the following about it:
1
f (1) = 2, f 0 (1) = 0, f (2) (1) = 5, f (3) (1) = 1, f (4) (x) = x
x5
1
Write an algebraic expre
Math 231 Worksheet #17 Solutions
P
1. Can you use the Ratio test to determine the convergence of
n=1
not?
Solution:
1
4
an+1
4
n
= lim (n+1) = lim
Ratio Test: lim
=1
n
an n 1 n n + 1
1
.
n4
Math 231 Worksheet #22 Solutions
1. (Dif. Eq). Power series can be used to solve differential equations. Suppose that a
country has at time t a population p(t), and that the rate of change of the popu
Math 231 Worksheet #16 Solutions
1. Determine if the series is absolutely convergent, conditionally convergent or divergent.
X
n2 n + 1
(a)
n5 + 300n3 + 2
n=0
Solution:
2
Since nn5 = 1n this series wi
Study Guide for U.S. History Final Exam
Brown v. Board of Education A 1954 case in which the Supreme
Court ruled that separate but equal education for black and white
students was unconstitutional.
Influential Person Essay
Bouncing down the dirt road next to the early morning fog resting on the lakes
surface, we rode in the hayride and listened to the hum of the tractor engine. Loose
wooden boar
Questions: 1. The ways solar panels work is from the energy generated from photons hitting the surface a solar panel. This makes the electrons pushed out of their orbits and released, and electric fie
1. Show that for any number r 6= 1,
1 + r + r2 + + rn =
1 rn+1
1r
2. Which of the following expressions would be used to determine the partial fraction
decomposition of
1
?
(x2 1)(x2 + 3)
B
Cx + D
A
+