{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

09Ff - Prof Girardi Math 554 Fall 2009 Friday December 11...

This preview shows pages 1–2. Sign up to view the full content.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Prof. Girardi Math 554 Fall 2009 Friday December 11 at 2:00 p.m. Final Exam From our textbook: Introduction to Real Analysis by William F. Trench 2.1.4e Find lim x → x f ( x ) and justify your answer with an- δ proof. f ( x ) = x 3- 1 ( x- 1)( x- 2) + x , x = 1 2.1.7d Find lim x → x- f ( x ) and lim x → x + f ( x ), if they exist. Use- δ proofs, where applicable, to justify your answers. f ( x ) = x 2 + x- 2 √ x + 2 , x = – 2 2.1.11 Prove: If lim x → x f ( x ) = L > 0, then lim x → x p f ( x ) = √ L . 2.1.17c Use an- M definition of lim x →∞ f ( x ) = L to show that lim x →∞ sin x does not exist. 2.1.20b Find, and then prove using the appropriate limit definition, lim x → – 1 x 3 . 2.2.9 The characteristic function ψ T : R → R of a set T is defined by ψ T ( x ) = ( 1 , x ∈ T , x / ∈ T . Show that ψ T is continuous at a point x ∈ R if and only if x ∈ T o ∪ ( T C ) o ....
View Full Document

{[ snackBarMessage ]}

Page1 / 2

09Ff - Prof Girardi Math 554 Fall 2009 Friday December 11...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online