Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta
    • Thread Starter
    Offline

    1
    ReputationRep:
    Can anyone help me with these practice questions?

    1)

    Given that y = x^(sinhx)

    prove:

    y.d²y/dx² - (dy/dx)² = y² / x


    2)

    Given that sinhx = tant 0 < tant t < (pi)/2

    Prove:

    i) tanhx = sint

    ii) e^x = sect + tant


    Cheers. I could do them yesterday and now i cant and can't find my notes. I hope i don't forget stuff in the exam. :rolleyes:
    Offline

    0
    ReputationRep:
    What does ^ mean? And what exam board are you doing? Because I've never seen questions lke that in my life and I'm doing OCR P5 on monday!
    Offline

    0
    ReputationRep:
    it means to the power of, 2^2 = 4
    • Thread Starter
    Offline

    1
    ReputationRep:
    well i'm doing edexcel, but hyperbolics and differentiation/integrastion are both on the ocr p5 syllabus, so it should resemble your work...
    Offline

    0
    ReputationRep:
    I've done a question like the second one. Have you tried squaring it and then using identities? Although the question i did was prove that coshx = sect and the second part is just using the relationship you proved in the first part.

    As for the first question I'd suggest taking logs and then using implicit differentiation and the product rule.
    Offline

    0
    ReputationRep:
    The first question is a mistake, I have come across it on another forum on which somebody said they had rung up Heinmann who confirmed the question was wrong. It should be y=x^x, rather than y=x^(sinhx).
    Offline

    1
    ReputationRep:
    (Original post by mikesgt2)
    The first question is a mistake, I have come across it on another forum on which somebody said they had rung up Heinmann who confirmed the question was wrong. It should be y=x^x, rather than y=x^(sinhx).
    yup ... my maths teacher said tht too ... the answer at the backis wat it should b for x^x
    Offline

    2
    ReputationRep:
    (Original post by SUKBarracuda)

    2)

    Given that sinhx = tant 0 < tant t < (pi)/2

    Prove:

    i) tanhx = sint

    ii) e^x = sect + tant
    i)
    tanhx = sinhx/coshx = tant/coshx

    and cosh^2 x - sinh^2 x = 1
    so coshx = root(1 + sinh^2 x) = root(1+tan^2 t) = root(sec^2 t) = sect

    so tanhx = sinhx/coshx = tant/coshx = tant/sect
    rearrange it and you ll get sint

    ii)from above, coshx = sect
    so sect + tant = coshx + sinhx = e^x
 
 
 
Turn on thread page Beta
Updated: June 20, 2004
Poll
Are you going to a festival?
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.