Calculus Homework

User Generated

bssvpvnywbagre

Mathematics

Description

Calculus exam.

Show your work.

......................................................

Unformatted Attachment Preview

MTH 174 Test 3 – show your work (do not just answer the question with one word. Explain your reasoning) Name 1. Determine the following infinite sequences whether converges or diverges. If it converges, compute the limit. 𝑛! a. { 𝑛𝑛 } b. { √𝑛 + 47 − √𝑛 } 𝑛2 +1 c. { (𝑛+1)2 } 2𝑛 d. { 𝑛! } e. { sin 𝑛2 𝑛2 } 2. Given the following infinite series determine if they are convergent or divergent (show your work on how you come to the decision) 1 a. ∑ 𝑛 ln(𝑛) (sin 𝑛)2 𝑛2 1 ∑ 𝑛 𝑒 𝑛 ∑ 2 𝑛 +1 ∑(−1)𝑛 b. ∑ c. d. e. f. g. h. i. 1 2𝑛+5 ln(𝑛) ∑(−1)𝑛 𝑛 1 ∑ 2 2𝑛 +3𝑛+1 3𝑛+1 ∑ 2 2𝑛 +3𝑛+1 ln 𝑛 ∑ 2𝑛 3. Determine whether each series converges absolutely, converges conditionally, or diverges. (−1)𝑛 a. ∑ 2𝑛2+5𝑛+1 b. ∑ c. d. (−1)𝑛 (3𝑛2 +𝑛−5) 2𝑛2 +5𝑛+1 3𝑛 ∑(−1)𝑛 𝑛 𝑛 2 +5 arctan 𝑛 ∑(−1)𝑛 𝑛 4. Write down the Taylor polynomials expansion up to the 𝑥 4 term at give center, and then attach the plot on Desmos (of the given function and its Taylor polynormial) 𝑥+1 ) find 𝑥−1 a. Given 𝑔(𝑥) = ln( its McLaurin polynomial (aka at x = 2) b. Given ℎ(𝑥) = 𝑒 −2𝑥 find its Taylor polynomial at x = -1 c. Given ℎ(𝑥) = 𝑡𝑎𝑛−1 (2𝑥), find its McLaurin expansion (aka at x = 0) 5. For each infinite series, find its, center, radius of convergence, and interval of convergence (note that you need to check the end points) 𝑛 a. Let ∑∞ 𝑛=1(−1) 3𝑛 (𝑥−2)𝑛 2𝑛 +5𝑛 3𝑛 (𝑥+1)𝑛 ∑(−1)𝑛 𝑛𝑛 𝑛 𝑛 3 𝑥 ∑ (𝑛+1)! b. ∑ c. d. (𝑥+1)𝑛 3𝑛
Purchase answer to see full attachment
User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.

Explanation & Answer

Fini...


Anonymous
Really helped me to better understand my coursework. Super recommended.

Studypool
4.7
Trustpilot
4.5
Sitejabber
4.4

Related Tags