# University of California Advanced Calculus of One Real Variable Exam Practice

Description

DVANCED CALCULUS 1,Basic topology of the real line, numerical sequences and series, continuity, differentiability, Riemann integration, uniform convergence, power series.

1 attachmentsSlide 1 of 1attachment_1attachment_1

Unformatted Attachment Preview

QUIZ 4. ADVANCED CALCULUS 1, FALL 2020
1. (5 pts) Suppose that the sequence {xn } is increasing and has a
convergent subsequence. Does {xn } necessarily have a limit? Prove
2. (5 pts) Which three of the following statements, if combined,
imply that the sequence {x2n−1 }∞

(A) the sequence {xn }n=1 is bounded
(B) |xn − xn+100 | < n1 for every n ∈ N (C) the sequence {x2n }∞ n=1 is increasing 1 (D) |xn − xn+101 | < n for every n ∈ N 3. (5 pts) Use the Cauchy criterion to prove that the sequence converges 1 1 1 xn = 1 + 2 + 2 + ... + 2 . 2 3 n Hint: Use the inequality 1 1 1 < − . 2 n n−1 n 1 Purchase answer to see full attachment Tags: sequence converges Cauchy sequence convergent subsequence theorem limit limit behavior User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.

## Reviews, comments, and love from our customers and community:

This page is having a slideshow that uses Javascript. Your browser either doesn't support Javascript or you have it turned off. To see this page as it is meant to appear please use a Javascript enabled browser.

Peter M.
So far so good! It's safe and legit. My paper was finished on time...very excited!
Sean O.N.
Experience was easy, prompt and timely. Awesome first experience with a site like this. Worked out well.Thank you.
Angela M.J.
Good easy. I like the bidding because you can choose the writer and read reviews from other students
Lee Y.
My writer had to change some ideas that she misunderstood. She was really nice and kind.
Kelvin J.
I have used other writing websites and this by far as been way better thus far! =)
Antony B.
I received an, "A". Definitely will reach out to her again and I highly recommend her. Thank you very much.