Exam (elaborations)
MAT272 Test3A SP19 KEY.
MAT272 Test3A SP19 KEY. MAT272 Test3A SP19 KEY. MAT272 Test3A SP19 KEY.
[Show more]
Content preview
Math 272 Test 3A Spring 2019 Name: KEYClearly indicate your method of solution for full credit. Clearly indicate your final answers. Time limit is 100 minutes.
Non-graphing calculators allowed. (8 points)
1. Complete the following table, using DNE (does not exist) as necessary.
Sequence Increasing, Decreasing or Bounds lim 𝑎𝑛
𝑛→∞
Neither?
1
n 1 Neither Upper: 0
an n
, n 1 1/2 (or larger)
2
Lower:
-1/4 (or smaller)
n Increasing Upper: 1
an , n 1 1 (or larger)
n3
Lower:
1/4 (or smaller)
2. Find the explicit formula for the 𝑛𝑡ℎ term of the sequence below.
2 4 8 16 32
, , , , ... (4 points)
7 12 17 22 27
(−𝟏)𝒏+𝟏 𝟐𝒏
𝒂𝒏 =
𝟐 + 𝟓𝒏
This study source was downloaded by 100000845196002 from CourseHero.com on 05-26-2022 14:00:48 GMT -05:00
https://www.coursehero.com/file/40300117/MAT272-Test3A-SP19-KEYpdf/
, 3. Use a convergence test of your choice to determine whether the following series converges absolutely, converges
conditionally or diverges. State the test you used and show all work. (7 points)
1
k
k 2 ln k
Test for absolute convergence:
(−𝟏)𝒌 𝟏 𝟏
Comparison Test: |
𝒍𝒏 𝒌
| = 𝒍𝒏 𝒌 > 𝒌 (diverges)
The series does not converge absolutely.
Test for conditional convergence:
Alternating Series Test:
𝟏 𝟏 𝟏
1) 𝐥𝐧 𝒌
is decreasing since 𝐥𝐧(𝒌+𝟏) < 𝐥𝐧 𝒌
𝟏
2) 𝐥𝐢𝐦 𝐥𝐧 𝒌 = 𝟎
𝒌→∞
The series does converge conditionally.
Therefore the series converges conditionally (but not absolutely).
4. Calculate and write the partial sum of the first four non-zero terms of the Taylor Series representation of
f ( x) e3 x centered at a 2 . (8 points)
𝒏 𝒇(𝒏) (𝒙) 𝒇(𝒏) (𝟐)
0 𝒆𝟑𝒙 𝒆𝟔
1 𝟑𝒆𝟑𝒙 𝟑𝒆𝟔
2 𝟗𝒆𝟑𝒙 𝟗𝒆𝟔
3 𝟐𝟕𝒆𝟑𝒙 𝟐𝟕𝒆𝟔
𝒆𝟔 𝟑𝒆𝟔 𝟗𝒆𝟔 𝟐𝟕𝒆𝟔
𝑻𝟑 (𝒙) = (𝒙 − 𝟐)𝟎 + (𝒙 − 𝟐)𝟏 + (𝒙 − 𝟐)𝟐 + (𝒙 − 𝟐)𝟑
𝟎! 𝟏! 𝟐! 𝟑!
𝟗 𝟗
𝑻𝟑 (𝒙) = 𝒆𝟔 + 𝟑𝒆𝟔 (𝒙 − 𝟐) + 𝟐 𝒆𝟔 (𝒙 − 𝟐)𝟐 + 𝟐 𝒆𝟔 (𝒙 − 𝟐)𝟑
This study source was downloaded by 100000845196002 from CourseHero.com on 05-26-2022 14:00:48 GMT -05:00
https://www.coursehero.com/file/40300117/MAT272-Test3A-SP19-KEYpdf/
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller royalmarsden. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for £7.49. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
67232 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy revision notes and other study material for 14 years now