rev1 - S (a) := X n =0 5 n ( n !) 2 (2 n !) , S (b) := X n...

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

Physics (PHZ) 3113 Florida Atlantic University Mathematical Physics Fall, 2009 Review Problems I Recommended Reading: Chow, Appendix 1; Boas, Chapter 1. 1. (Chow A1.7, p. 510) Prove that sin 2 x = 1 - cos 2 x 2 and cos 2 x = 1 + cos 2 x 2 , and that A cos x + B sin x = p A 2 + B 2 sin( x + δ ) , where tan δ := A B for all real x , A and B . 2. (Chow A1.8, p. 510) Prove that cosh 2 x - sinh 2 x = 1 and sech 2 x + tanh 2 x = 1 for all real x . 3. (Chow A1.9, p. 511) Calculate the limit of the function f ( x ) := x 2 as x 2, and show that f ( x ) is continuous there. 4. (Boas 1.4.6) Evaluate the partial sums S N := N X n =1 1 n ( n + 1) , and show that they converge in the limit N → ∞ . Hint : Expand the summand using partial fractions. 5. (Boas 1.6.4) Use the comparison test to prove that series S (a) := X n =1 1 2 n + 3 n and S (b) := X n =1 1 n 2 n . converge. 6. (Boas 1.6.8 and 14) Use the integral test to determine whether the series S (a) := X n =1 n n 2 + 4 and S (b) := X n =1 1 n 2 + 9 converge or diverge.

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

View Full Document
7. (Boas 1.6.21, 26 and 29) Use the ratio test to determine whether the series
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: S (a) := X n =0 5 n ( n !) 2 (2 n !) , S (b) := X n =0 ( n !) 3 e 3 n (3 n )! and S (c) := X n =0 p (2 n )! ( n )! converge or diverge. 8. (Boas 1.17.1, 4 and 6) Use the alternating series test to determine whether the series S (a) := X n =1 (-1) n n , S (b) := X n =1 (-3) n n ! and S (c) := X n =1 (-1) n n n + 5 converge or diverge. 9. Which of the series from the previous problem converge absolutely? 10. (Chow A1.13, p. 520) Use Gauss test to determine whether the series S := 1 2 2 + 1 3 2 4 2 + 1 3 5 2 4 6 2 + converges or diverges. Show that neither the ratio test nor Raabes test would be conclusive for this series....
View Full Document

This note was uploaded on 10/21/2011 for the course PHZ 3113 taught by Professor Staff during the Fall '10 term at FAU.

Page1 / 2

rev1 - S (a) := X n =0 5 n ( n !) 2 (2 n !) , S (b) := X n...

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

View Full Document
Ask a homework question - tutors are online