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
Unformatted text preview: Math 119 Week 2 Solutions 1 1. Guessing δ For given > 0, we want to find δ > 0 such that  (2 x + 3) 5  < whenever  x 1  < δ ⇒  2( x 1) < whenever  x 1  < δ ⇒  x 1  < 2 whenever  x 1  < δ Thus, we can choose δ = 2 Showing that this δ works ∀ > ∃ δ = 2 such that  (2 x + 3) 5  < whenever  x 1  < δ = 2  (2 x + 3) 5  =  2 x 2  = 2  x 1  < 2 . 2 = 2. Guessing δ For given M , we want to find δ > 0 such that  1 ( x + 3) 4  > M whenever  x ( 3)  < δ ⇒  ( x + 3) 4  < 1 M whenever  x + 3  < δ ⇒  ( x + 3)  < 4 r 1 M whenever  x + 3  < δ so, we can choose δ = 4 r 1 M Showing that this δ works ∀ > ∃ δ = 4 r 1 M such that  1 ( x + 3) 4  > M whenever  x ( 3)  < δ = 4 q 1 M  1 ( x + 3) 4  > 1 δ 4 = 1 ( 4 q 1 M ) 4 = M 3. We want that f ( x ) is continuous on (∞ , ∞ ). Obviously f ( x ) is continu ous on (∞ , 3) and (3 , ∞ ), because f ( x ) is defined as a polinomial on the ray (∞ , 3) or (3 , ∞ ). Thus, it is enough that lim)....
View
Full
Document
This note was uploaded on 03/31/2010 for the course MATHEMATIC 119 taught by Professor Muhiddinuğuz during the Fall '08 term at Middle East Technical University.
 Fall '08
 muhiddinuğuz
 Math, Calculus, Geometry

Click to edit the document details