{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# review2 - MAC 3473 FALL 2007 REVIEW PROBLEMS FOR TEST 2 1...

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

MAC 3473 - FALL 2007 REVIEW PROBLEMS FOR TEST 2 1 . Determine whether each of the following integrals is convergent or divergent. Be sure to show your work and explain your reasoning. a) Z 5 dx x (ln x ) b) Z 2 x 14 + 1 x 15 - x dx c) Z 4 1 dx 4 - x d) Z 1 0 ln x x dx 2 . Determine whether the following improper integrals convergent or divergent. Be sure to show your work and explain your reasoning. a) Z 0 dx ( x + 1)( x + 3) b) Z 0 dx (4 + x 2 ) 3 / 2 c) Z 1 0 dx (1 - x 4 ) 1 / 12 3 . (i) Define what it means for the number L to be a limit of the sequence { a n } n =1 . (ii) Prove the following limits using the formal definition. a) lim n →∞ 1 3 n + 1 = 0 , b) lim n →∞ 3 n - 1 2 n + 1 = 3 2 . (iii) Determine whether the following sequences converge, giving reasons. Find limit if it exists. a) a n = ( n + 1)( n + 2) ( n + 3)( n + 4) b) b n = ( - 1) n cos(1 /n ) c) c n = n + 2 - n - 1 d) d n = n e n e) e n = (3 n ) 1 /n (iv) State the Squeeze Theorem. (v) Use the Squeeze Theorem to prove that lim n →∞ e cos n n = 0 .

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.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern