Turn on thread page Beta
    • Thread Starter
    Offline

    6
    ReputationRep:
    I don't know what to do for question 5
    Attached Images
     
    Offline

    1
    ReputationRep:
    Try to visualise these functions: hopefully you know that a root of f(x)-g(x)=0 means finding a point of intersection of f(x) and g(x). So sin(x-6) is very close to sin(x-2pi) which is very close to sin(x). Equally, ln(x^2+1) translates the curve such that its root is at the origin, and the x^2 means it looks like a ln(x) graph forward and back (even function). Draw them or use a graphing software to see that they will cross near the start.

    At this stage, try the value k=1 since it is the lowest positive integer. Calculate f(1) and f(2) and the change of sign proves that a root exists in the boundary (1,2).

    For part (b), write sin(x-6)=ln(x^2+1), then remove the log by taking e^LHS = e^RHS. Rearrange and you're done.
    Offline

    11
    ReputationRep:
    For part a what they are looking for is two integers between which sin(x-6)-ln(x^2+1) changes sign. Hence there is a root in between. This gives k.
    For b, all you have to do is use the iteration formula
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: November 2, 2016
The home of Results and Clearing

2,563

people online now

1,567,000

students helped last year

University open days

  1. Bournemouth University
    Clearing Open Day Undergraduate
    Wed, 22 Aug '18
  2. University of Buckingham
    Postgraduate Open Evening Postgraduate
    Thu, 23 Aug '18
  3. University of Glasgow
    All Subjects Undergraduate
    Tue, 28 Aug '18
Poll
How are you feeling about GCSE results day?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.