{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Test1_with_solutions

# Test1_with_solutions - 1(12 points For each sequence below...

This preview shows pages 1–3. Sign up to view the full content.

1. (12 points) For each sequence below either calculate the limit or write “does not converge”: a. lim n - > n 3 (2 n - 1) 3 ANS: This converges to 1 8 as this is the ratio of the coefficients of the leading terms and the polynomials have the same degree. b. lim n - > ne - 3 n ANS: This converges to 0. We can think of e - 3 n as either exponential decay, or as an exponential function on the bottom of a fraction. c. lim n - > ( - 1) n + 1 n ANS: The first term ( - 1) n oscillates, and the second term goes to zero, so their sum doesn’t converge. d. lim n - > sin( ( - 1) n n ) ANS: This converges to 0. To do this one you had to remember that: lim n - > sin( ( - 1) n n ) = sin(lim n - > ( - 1) n n ) because sin is continuous. lim n - > ( - 1) n n = 0 . sin(0) = 0 . 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2. (14 points) Place each sequence in the appropriate place on the following list by either putting the sequence in the same box as a sequence that has the same rate of growth putting a sequence between two boxes, to say that its rate of growth is slower
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 5

Test1_with_solutions - 1(12 points For each sequence below...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online