05sprg-final

05sprg-final - MAT 371 May 8, 2005 1 Advanced Calculus...

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

View Full Document Right Arrow Icon
MAT 371 Advanced Calculus /160 May 8, 2005 Final Exam name 1 2 3 4 5 6 7 8 20 20 20 20 20 20 20 20 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 1. Give precise definitions of five technical terms (these may be nouns, adjectives, verbs, or surnames) from our class that start with the letter “c”. You may choose the context (e.g., subsets, sequences in metric spaces, or real-valued functions – but you must be precise). 2. a. State the supremum (or “least upper bound” ) axiom for the real numbers. Define the technical terms that you use in the axiom. b. State the mean value theorem of differential calculus. c. State a major theorem that involves both “compact” and “continuous” . 3. a. Suppose that ( a n ) n =1 is a sequence in a metric space ( X,d ). Prove that if the sequence ( a n ) n =1 has a limit, then this limit is unique. b. Give an example that shows that the set { a n : n Z + } of values of a sequence ( a n ) n =1 in a metric space ( X,d ) can have more than one limit point. Justify your assertions.
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/02/2009 for the course MAT 371 taught by Professor Thieme during the Spring '07 term at ASU.

Ask a homework question - tutors are online