{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

test1_(in_class) - a n 1 = 1 1 1 a n n ∈ N where a 1 = 1...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Test 1 (In class part), MAA4226 Fall 2010 Student Name: 60 minutes. Closed book. This part weighs 40% of the total weight of Test 1. 1: State and prove the extreme value theorem. 2: Let { a n } be a sequence such that lim n →∞ a 2 n = lim n →∞ a 2 n +1 = l . Show that lim n →∞ a n = l . 3: Let { a n } be the sequence defined by the recurrence relation
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: a n +1 = 1 + 1 1 + a n , n ∈ N , where a 1 = 1. Use problem 2 above to show that { a n } is convergent and find its limit. 3: Let f : [0 , 1] → R be continuous and one-to-one. Show that f is strictly monotone. 1...
View Full Document

{[ snackBarMessage ]}