Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    2
    ReputationRep:
    http://www.ocr.org.uk/Images/65004-q...hematics-2.pdf

    I'm a bit stuck on question 2. So I've found the macluren series for e^{2x} and for sin(x). But then I'm not to sure what to do, I expanded out the binomial to get the first 3 terms not sure if it's right...
    • Community Assistant
    Offline

    20
    ReputationRep:
    Community Assistant
    Post your working.

    Work out the expansion of e^{2x} (1+\sin x) first though (multiply your previous results).
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by Mr M)
    Post your working.

    Work out the expansion of e^{2x} (1+\sin x) first though (multiply your previous results).
    So we have  e^{2x}=1+2x+\frac{2x^2}{2!}+...
    sin(x)=x-\frac{x^3}{3!}+\frac{x^5}{5!}+..  .

    So (1+sinx)e^{2x}=e^{2x}+sinxe^{2x}  =1+2x+\frac{2x^2}{2!}+...+(x-\frac{x^3}{3!}+\frac{x^5}{5!})(1  +2x+\frac{2x^2}{2!})
    • Community Assistant
    Offline

    20
    ReputationRep:
    Community Assistant
    (Original post by Music99)
    So we have  e^{2x}=1+2x+\frac{2x^2}{2!}+...
    sin(x)=x-\frac{x^3}{3!}+\frac{x^5}{5!}+..  .

    So (1+sinx)e^{2x}=e^{2x}+sinxe^{2x}  =1+2x+\frac{2x^2}{2!}+...+(x-\frac{x^3}{3!}+\frac{x^5}{5!})(1  +2x+\frac{2x^2}{2!})
    Blimey you are making that too complicated. You don't need so many terms. Read the question.

    Add 1 to your expansion to sin x to find the first bracket.

    Multiply the terms and simplify.
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by Mr M)
    Blimey you are making that too complicated. You don't need so many terms. Read the question.

    Add 1 to your expansion to sin x to find the first bracket.

    Multiply the terms and simplify.
    Yeah I was thinking that as I was typing it out. So then for the first bracket it's just 1+x-\frac{x^3}{3!}?
    • Community Assistant
    Offline

    20
    ReputationRep:
    Community Assistant
    (Original post by Music99)
    Yeah I was thinking that as I was typing it out. So then for the first bracket it's just 1+x-\frac{x^3}{3!}?
    Yes. Simplify 3! to 6. You won't need that x^3 term in the end.
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by Mr M)
    Yes. Simplify 3! to 6. You won't need that x^3 term in the end.
    Okay, I'll play around with it and post back If I have any questions or get stuck. Thanks for the help. I really need to get the textbook it sucks not having it aha.
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by Mr M)
    Yes. Simplify 3! to 6. You won't need that x^3 term in the end.
    I got it right . Thank you. Would you mind helping me on question 5 also?

    I'm on the first part. I've integrated by parts to get

    (1-2x)^n(e^x)+2n\int(1-2x)^{n-1}(e^x)dx Limits are 1/2 and 0,but I don't know how to latex them. I simplified it down to by saying the integral is just 2nI_{n-1} , although I'm not sure if that's right, or do I just integrated again?
 
 
 
Poll
Do you agree with the PM's proposal to cut tuition fees for some courses?
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.