Practice Test 2a solutions

# Practice Test 2a solutions - Solution to Practice Test IIA...

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

Solution to Practice Test IIA I: a) Has a solution since f (0) = 4 and f (8) = - 2 where f ( x ) = x 1 / 3 - x + 4 using Bolzano’s theorem. b) Has an inverse on the interval (0 , 1]. c) True d) True e) For y > 0, y 1 + ln( y ) . II: a) 2 / 3, b) 1 / 2, c) 0, d) 1 /e , e) 1 III: First start with some hypothetical considerations. Solving the equation c = 3 c + 4 the limit will be presumaby 4 (the sequence is always positive. Presumably, the sequence will decrease from 5 towards 1. Therefore we conjecture that the sequence will decrease from 5 towards 4 and the limit will be 4. a) First we show that the sequence is bouncec below by 4, i.e., a n 4. We proceed by induction: a 1 = 5 > 4. Assuming a n 4 for some n we have to show that a n +1 4. To see that write a n +1 - 4 = 3 a n + 4 - 4 = 3( a n - 4) 3 a n + 4 + 4 0 . b) Next we show that the sequence is monotone decreasing: a n - a n +1 = a n - 3 a n + 4 = a 2 n - 3 a n - 4 a n + 3 a n + 4 = ( a n - 4)( a n + 1)

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.

## This note was uploaded on 02/07/2011 for the course MATH 1501 taught by Professor N/a during the Fall '08 term at Georgia Institute of Technology.

### Page1 / 2

Practice Test 2a solutions - Solution to Practice Test IIA...

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

View Full Document
Ask a homework question - tutors are online