This preview shows pages 1–3. 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: Time allowed: 20 minutes. 1. (4 marks) Let f ( x ) = x 2 . (a) If a > 0, find lim x a f ( x ). (b) Prove your answer in (i) by arguing in terms of and . 2. (2 marks) Find lim x 1 cos 3 x x 2 . 3. (2 marks) Consider the function f ( x ) = x 4 4 x 3 11 x 2 + 30 x x a . This is not continuous at x = a . For what values of a is the discontinuity removable? 4. (2 marks) State the Mean Value Theorem. Hence or otherwise, show that x sin 1 x for 1 < x 0. Version 2, 4/5/08 Week 7 Tuesday 1011 Class 1. (a) lim x a f ( x ) = a 2 . (b) lim x a f ( x ) = l means: For all real numbers > 0, there exists a real number > 0, such that:  f ( x ) l  < whenever 0 <  x a  < . Let > 0 be given. We want to find > 0 such that  x 2 a 2  < whenever 0 <  x a  < . Now  x 2 a 2  =  x a  x + a  . Lets assume  x a  < a....
View
Full
Document
 Three '11

Click to edit the document details