MATH1151 week7c3

# MATH1151 week7c3 - Time allowed: 20 minutes. 1. (4 marks)...

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
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 − x for − 1 ≤ x < 0 and f ( x + 1) = f ( x ) for all x ∈ R . (a) Find an expression for f ( x ) for 0 ≤ x < 1. (b) Prove that f is continuous at 0. That is, prove lim x → f ( x ) = f (0). (c) Does f (0) exist? Prove your answer. If it does exist, what is its value? 2. (3 marks) (a) State the Mean Value Theorem. (b) Use the Mean Value Theorem to show that, for all real x and y , | tan − 1 x − tan − 1 y | ≤ | x − y | . 3. (2 marks) It is given that 0 < < 1 2 , and the solution to | f ( x ) − 2 | < is x ∈ −∞ , − 1 − 2 ∪ 1 − 2 , ∞ . Does lim x →∞ f ( x ) exist? If so, what is its value? Give reasons for your answer. 4. (1 mark) Explain why cosh( x + h ) = cosh x + h sinh( x ) + o ( h ) as h → 0. Week 7 Friday 11-12 Class 1. f ( x ) = x 3 − x = x ( x − 1)( x + 1) for − 1 ≤ x < 0, and f ( x + 1) = f ( x ) for all x ∈ R ....
View Full Document

## This document was uploaded on 03/19/2012.

### Page1 / 3

MATH1151 week7c3 - Time allowed: 20 minutes. 1. (4 marks)...

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

View Full Document
Ask a homework question - tutors are online