You are Here: Home >< Maths

C3 hard question watch

1. I don't know what to do for question 5
Attached Images

2. 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.
3. 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

Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: November 2, 2016
The home of Results and Clearing

2,563

people online now

1,567,000

students helped last year
Today on TSR

GCSE results day guidance

All you need to know is here

University open days

1. Bournemouth University
Wed, 22 Aug '18
2. University of Buckingham
Thu, 23 Aug '18
3. University of Glasgow
Tue, 28 Aug '18
Poll
Useful resources

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

How to use LaTex

Writing equations the easy way

Study habits of A* students

Top tips from students who have already aced their exams

Chat with other maths applicants