Math 152 Exam 2 Concepts
0.0(0)
Studied by 0 people
Learn
Practice Test
Spaced Repetition
Match
FlashcardsCard Sorting
1/18
There's no tags or description
Looks like no tags are added yet.
Study Analytics
Name | Mastery | Learn | Test | Matching | Spaced |
|---|
No study sessions yet.
19 Terms
1
New cards
How would you solve a definite improper integral with bounds from negative infinity to positive infinity?
Split them up into an integral from negative infinity to 0 and 0 to infinity and then add them together
2
New cards
If you have an integral where the bounds are a to b and the function is discontinuous at 'b'...
When solving the integral you take the limit of the function approaching 'b' from the left
3
New cards
If you have an integral where the bounds are a to b and the function is discontinuous at 'a'...
When solving the integral you take the limit of the function approaching 'a' from the right
4
New cards
If you have an integral where the bounds are a to b and the function is discontinuous at a value in between the bounds ('c')...
When solving the integral you split the integral from 'a' to 'c' and then 'c' to 'b' and then add them together
5
New cards
For a p-integral...
p
6
New cards
(Comparison theorem) if bigger is convergent...
smaller is convergent
7
New cards
(Comparison theorem) if bigger is divergent...
the comparison test fails
8
New cards
(Comparison theorem) if smaller is divergent...
bigger is divergent
9
New cards
(Comparison theorem) if smaller is convergent...
the comparison test fails
10
New cards
(Sequences) if the limit as n approaches infinity exists...
the sequence converges
11
New cards
(Sequences) if the limit as n approaches infinity does not exist...
the sequence diverges
12
New cards
(Sequences) A(n) is decreasing if...
A(n) > A(n+1)
13
New cards
(Sequences) A(n) is increasing if...
A(n) < A(n+1)
14
New cards
As sequence is monotonic if...
it is neither increasing or decreasing
15
New cards
If the sequence is convergent...
The sequence is bounded!
16
New cards
What is the test for divergence?
If the limit of A(i) is not equal to zero or does not exist, the series is divergent
17
New cards
How do you find A(n) given S(n)?
Use the formula A(n) = S(n) - S(n-1)
18
New cards
What is the integral test?
Treating A(n) as F(n) and if the integral of F(n) converges then A(n) converges, and if the integral of F(n) diverges then A(n) diverges
19
New cards
What are the requirements for the integral test?
Must be continuous, positive, and decreasing on the interval from [1, oo) or [a, oo)
Note 
Flashcards (20)