MATH1151 week7c1 - Time allowed: 20 minutes. 1. (4 marks)...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

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

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

Unformatted text preview: Time allowed: 20 minutes. 1. (4 marks) The function f is defined by f ( x ) = x 3 for 1 < x 1 and f ( x + 2) = f ( x ) + 2 for all x R . (a) Find an expression for f ( x ) for 3 < x 1. (b) Prove that f is continuous at 1. That is, prove lim x 1 f ( x ) = f ( 1). (c) Does f ( 1) exist? Prove your answer. If it does exist, what is its value? 2. (1 mark) Explain why tan( x + h ) = h + tan( x ) + h tan 2 ( x ) + o ( h ) as h 0. 3. (3 marks) Let f ( x ) = e 2 x . (a) Find lim x f ( x ). (b) Prove your answer in (i) by arguing in terms of and M . 4. (2 marks) State the value of lim x tan x x . Hence, or otherwise, find lim x tan x x x 3 . Week 7 Monday 12-1 Class 1. f ( x ) = x 3 for 1 < x 1, and f ( x + 2) = f ( x ) + 2 for all x R . (a) For 3 < x 1 f ( x ) = f ( x + 2) 2 = ( x + 2) 3 2 = ( x 3 + 6 x 2 + 12 x + 8) 2 (by the Binomial Theorem) = x 3 + 6 x 2 + 12 x + 6 So for 3 < x...
View Full Document

This document was uploaded on 03/19/2012.

Page1 / 3

MATH1151 week7c1 - Time allowed: 20 minutes. 1. (4 marks)...

This preview shows document pages 1 - 3. Sign up to view the full document.

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