MIT18_014F10_pr_ex1

# MIT18_014F10_pr_ex1 - PRACTICE EXAM 1 103(1 Compute 99(2x...

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: PRACTICE EXAM 1 103 (1) Compute 99 (2x - 198)2 x - 99 dx where here [x] is defined to be the largest integer x. (2) Let S be a square pyramid with base area r2 and height h. Using Cavalieri's Theorem, determine the volume of the pyramid. (3) Let f be an integrable function on [0, 1]. Prove that |f | is integrable on [0, 1]. (4) The well ordering principle states that every non-empty subset of the nat ural numbers has a least element. Prove the well ordering principle implies the principle of mathematical induction. (Hint: Let S P be a set such that 1 S and if k S then k + 1 S. Consider T = P - S. Show that T = .) (5) Suppose limxp+ f (x) = limxp- f (x) = A. Prove limxp f (x) = A. 1 MIT OpenCourseWare http://ocw.mit.edu 18.014 Calculus with Theory Fall 2010 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. ...
View Full Document

## This note was uploaded on 01/18/2012 for the course MATH 18.014 taught by Professor Christinebreiner during the Fall '10 term at MIT.

### Page1 / 2

MIT18_014F10_pr_ex1 - PRACTICE EXAM 1 103(1 Compute 99(2x...

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

View Full Document
Ask a homework question - tutors are online