s41 - 2, then 2 - n is positive, so T = ( 1 + x 2 n- 2 + (1...

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

View Full Document Right Arrow Icon
Solution to Problem 41 This week’s problem went unsolved by the Bradley students. Ray Kremer submitted a partial solution. A correct solution was submitted by Philippe Fondanaiche who also correctly solved the more challenging problems. Sorry, Philippe, the dollar must go to a Bradley student! Refer to the diagram in the statement of the problem. Let P = ( x , y ), O denote the origin, and R = ( x ,0). The triangles TOQ and PRQ are similar, giving us s T = s - x y or T = sy s - x = sy ( s + x ) s 2 - x 2 . From the right triangle POR we get x 2 + y 2 = s 2 which after substituting and simplifying gives T = x n (Ö( x 2 + x 2 n )) (x + Ö( x 2 + x 2 n )) x 2 n = 1 + x 2 n - 2 + Ö(1 + x 2 n - 2 ) x n - 2 Now look at cases. If n <
Background image of page 1

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

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 2, then 2 - n is positive, so T = ( 1 + x 2 n- 2 + (1 + x 2 n- 2 ) ) x 2 - n with the first term going to 2 and the second term going to 0, as x 0. So T in this case. If n > 2, the term 1 + (1 + x 2 n- 2 ) x 2 n- 2 since the numerator approaches 2, as x goes to 0, while the denominator gets arbitrarily small. On the other hand x 2 n- 2 x n- 2 = x n 0 as x 0. So in this case T . Finally, if n = 2, then T = 1 + x 2 + (1 + x 2 ) 2. Finally we have the answer. T 0, if n < 2 2, if n = 2 if n > 2 This proves, I guess, that 2 is between 0 and . this page....
View Full Document

This note was uploaded on 03/01/2010 for the course MATH 301 taught by Professor Albertodelgado during the Spring '10 term at Bradley.

Page1 / 2

s41 - 2, then 2 - n is positive, so T = ( 1 + x 2 n- 2 + (1...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online