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Attachment 1 (15) - Lecture notes 12-15

Notes of various types done within the A in the class
Course

Hist & Historians (HIST 300)

29 Documents
Students shared 29 documents in this course
Academic year: 2019/2020
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Indiana State University

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Math 2 Crew

Test 5

In problems 1 and 2, evaluate the integral or show that it diverges.

  2. Find the volume of the solid formed when the region bounded by and the x-axis on the interval is revolved about the y-axis.

  3. Find the solution of the following differential equation with the given initial condition.

  4. The population of hawks nesting on an island is modeled by the initial value problem

(a) Find the solution of this initial value problem. Show all of your work. (b) Based on this model what happens to the hawk population in the long run?

  1. Consider the sequence

(a) Find the next two terms of the sequence. (b) Find an explicit formula for the general nth term of the sequence. (c) Find a recurrence relation that generates the sequence.

In problems 7 and 8, find the limit of the sequence or determine that the limit does not exist.

  2. Find the value of the geometric series or state that it diverges.

(a) (b)

  1. For the following telescoping series, find a formula for the nth partial sum Sn. Then evaluate to find the value of the series or state that it diverges.

1

4 x 2 + 1

dx 32

∞

∫

1

( )x− 12

dx 1

3

∫

f(x)= 1

[0, 8) ( 8 −x)2 3

y′(t)=e

2 t 3 y

, y( ) 0 = 2

dP dt

=0 40( −P), P( ) 0 = 5

1

2

, 3

4

, 7

8

, 15

16

⎧⎨ ,...

⎩

⎫

⎬

⎭

.

n 2 + 4 n 2 n

⎧

⎨

⎪

⎩⎪

⎫

⎬

⎪

⎭⎪

1 + 3

n

⎛

⎝⎜

⎞

⎠⎟

⎧ n ⎨

⎪

⎩⎪

⎫

⎬

⎪

⎭⎪

−e π

⎛

⎝⎜

⎞

⎠⎟

k

k= 1

∞

∑

2 k− 1 k= 33 k+ 1

∞

∑

limn→∞Sn

1

k= 1 ( )k+ 3 (k+ 4 )

∞

∑

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Attachment 1 (15) - Lecture notes 12-15

Course: Hist & Historians (HIST 300)

29 Documents
Students shared 29 documents in this course

University: Indiana State University

Was this document helpful?
Math 2 Crew
Test 5
In problems 1 and 2, evaluate the integral or show that it diverges.
1. 2.
3. Find the volume of the solid formed when the region bounded by and the x-axis on the
interval is revolved about the y-axis.
4. Find the solution of the following differential equation with the given initial condition.
5. The population of hawks nesting on an island is modeled by the initial value problem
(a) Find the solution of this initial value problem. Show all of your work.
(b) Based on this model what happens to the hawk population in the long run?
6. Consider the sequence
(a) Find the next two terms of the sequence.
(b) Find an explicit formula for the general nth term of the sequence.
(c) Find a recurrence relation that generates the sequence.
In problems 7 and 8, find the limit of the sequence or determine that the limit does not exist.
7. 8.
9. Find the value of the geometric series or state that it diverges.
(a) (b)
10. For the following telescoping series, find a formula for the nth partial sum Sn. Then evaluate to find
the value of the series or state that it diverges.
1
4x2+1
dx
32
∞
∫
1
x−1
( )
2dx
1
3
∫
f(x)=1
8−x
( )
2 3
0, 8
[
)
′
y(t)=e2t
3y,y0
( )
=2
dP
dt
=0.07 40 −P
( )
,P0
( )
=5
n2+4n
2n
⎧
⎨
⎪
⎩
⎪
⎫
⎬
⎪
⎭
⎪
1+3
n
⎛
⎝
⎜⎞
⎠
⎟
n
⎧
⎨
⎪
⎩
⎪
⎫
⎬
⎪
⎭
⎪
−e
π
⎛
⎝
⎜⎞
⎠
⎟
k
k=1
∞
∑
2k−1
3k+1
k=3
∞
∑
lim
n→∞
Sn
1
k+3
( )
k+4
( )
k=1
∞
∑

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