Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    I need help guys. I've been set about 100! C3 questions, literally! However, there are a few I just can't do. Could anybody point me in the right direction or show me how to do it.

    1) Prove that: sec²x + cosec²x = sec²x . cosec²x

    2) Solve: cot²2x + cosec2x -1 = 0

    3) Find the x-cordinates of the turning points on the curve y = (x² + 4) / (2x - x²)

    4) Differentiate and simplify y = squareroot(1-x) / squareroot(1+x)
    y = squareroot(3x +2) / 2x
    y = squareroot(x-5) / x

    5) Find f '(4) when f(x)= x(e^squarerootx)

    6) The volume, V, of a solid is given by V = x²(squarerrot(8-x)). fing the maximum value of V and the value of x at which this occurs. This one has given me nightmares, literally. How on EARTH!

    It all has to be in tomorrow. AARRRGGGHHH! Maths isn't my strongest point. Thanks for any help/guidence!!!!!
    Offline

    0
    ReputationRep:
    Check that;

    sec²x + cosec²x - sec²xcosec²x = 0
    Offline

    2
    ReputationRep:
    1) sec²x + cosec²x = sec²x . cosec²x
    1/cos²x + 1/sin²x = sec²x . cosec²x
    (cos²x + sin²x)/sin²xcos²x = sec²x . cosec²x

    as cos²x + sin²x = 1

    1/sin²xcos²x = sec²x . cosec²x
    • Thread Starter
    Offline

    0
    ReputationRep:
    I did things along that line, but forgot about that last part. Wow - thanks!
    Offline

    15
    ReputationRep:
    (Original post by hi there)
    I need help guys. I've been set about 100! C3 questions, literally! However, there are a few I just can't do. Could anybody point me in the right direction or show me how to do it.

    1) Prove that: sec²x + cosec²x = sec²x . cosec²x

    2) Solve: cot²2x + cosec2x -1 = 0

    3) Find the x-cordinates of the turning points on the curve y = (x² + 4) / (2x - x²)

    4) Differentiate and simplify y = squareroot(1-x) / squareroot(1+x)
    y = squareroot(3x +2) / 2x
    y = squareroot(x-5) / x

    5) Find f '(4) when f(x)= x(e^squarerootx)

    6) The volume, V, of a solid is given by V = x²(squarerrot(8-x)). fing the maximum value of V and the value of x at which this occurs.

    It all has to be in tomorrow. AARRRGGGHHH! Maths isn't my strongest point. Thanks for any help/guidence!!!!!
    For 1, my initial thought is to try and get a common denominator on the bottom and see if you can do anything from there... it does work out.

    For 2) - use the identity that sin^2 + cos^2 =1 to try an equation involving cot^2 and cosec^2 . Substitute that into the original, and solve. Should end up being a quadratic.

    3 - Factorise top and bottom, simplify, differentiate using the quotient rule and take it from there.

    4 - Differentiate using combinations of the chain rule and quotient rule, i would have thought.

    5 - differentiate using a combo of the product rule and chain rule, then sub x = 4 into the equation.

    6 - once again, differentiate using a combination of product rule and chain rule, then you should be able to take it from there, keeping in mind that max/min values is a C2 skill.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by chidona)
    3 - Factorise top and bottom, simplify, differentiate using the quotient rule and take it from there.

    4 - Differentiate using combinations of the chain rule and quotient rule, i would have thought.

    5 - differentiate using a combo of the product rule and chain rule, then sub x = 4 into the equation.

    6 - once again, differentiate using a combination of product rule and chain rule, then you should be able to take it from there, keeping in mind that max/min values is a C2 skill.
    I've tried doing all of these but the maths and woking is all too complicated for me
    Offline

    2
    ReputationRep:
    2) Solve: cot²2x + cosec2x -1 = 0

    cot²x= 1 + cosec²x
    therefore
    cot²2x= 1 + cosec²2x

    1 + cosec²2x + cosec2x -1 = 0
    cosec²2x + cosec2x = 0
    cosec2x(cosec2x + 1)= 0

    etc
    • Wiki Support Team
    Offline

    14
    ReputationRep:
    Wiki Support Team
    (Original post by hi there)
    I've tried doing all of these but the maths and woking is all too complicated for me
    Post your working and we can help you further, we discourage giving out full solutions on here.
    Offline

    0
    ReputationRep:
    (Original post by hi there)
    3) Find the x-cordinates of the turning points on the curve
    y = (x² + 4) / (2x - x²)
    y(2x - x²) = (x² + 4)
    2xy - x²y = x² + 4,
    2y+2xy' - x²y' - 2xy = 2x (by implicit differentiation and y' = dy/dx)
    y' = 2(x+xy-y)/(2x-x²), set y' = 0
    0 = 2x+2xy-2y
    0 = x+y(x-1)
    0 = x+((x² + 4)(x-1))/(2x - x²)
    0 = x(2x - x²) + (x² + 4)(x-1)
    0 = 2x² - x^3 + x^3 - 4
    0 = x² - 2 = (x-rt2)(x+rt2)

    x = rt2 and x = -rt2
    Offline

    2
    ReputationRep:
    For 3 use quotient rule
    y = (x² + 4) / (2x - x²)

    where y=u/v

    let u=x² + 4 and v=2x - x²

    thus du/dx=2x and dv/dx=2-2x

    then use the formula to find dy/dx

    then let dy/dx=0 and rearrange for x

    once you have found x sub into original equation to find corresponding y value thus getting stationary coordinates!
    • Wiki Support Team
    Offline

    14
    ReputationRep:
    Wiki Support Team
    I really ought to start neg repping people for this.
    • Thread Starter
    Offline

    0
    ReputationRep:
    This may be dumb question, but what does "rt" mean?
    • Thread Starter
    Offline

    0
    ReputationRep:
    I'm sorry 'generalebreity'. Please don't give anybody neg rep!! I didn't know it was "wrong", but saying that i haven't read your sticky thread on the maths forum. I'll post my solutions in future.
    • Wiki Support Team
    Offline

    14
    ReputationRep:
    Wiki Support Team
    (Original post by hi there)
    I'm sorry 'generalebreity'. Please don't give anybody neg rep!! I didn't know it was "wrong", but saying that i haven't read your sticky thread on the maths forum. I'll post my solutions in future.
    "rt" = square root, I assume.

    I'm not talking about you, I'm talking about people like Decota who blatantly know better and are posting full solutions just to piss me off.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by Thaiprawns)
    For 3 use quotient rule
    y = (x² + 4) / (2x - x²)

    where y=u/v

    let u=x² + 4 and v=2x - x²

    thus du/dx=2x and dv/dx=2-2x

    then use the formula to find dy/dx

    then let dy/dx=0 and rearrange for x

    once you have found x sub into original equation to find corresponding y value thus getting stationary coordinates!
    I did all of that, but the problem is when you put it altogether, whith one big messy equation which is hard to rearrange!
    Offline

    2
    ReputationRep:
    question 4 uses the same concepts as question 3

    As for question 5
    Find f '(4) when f(x)= x(e^squarerootx)

    y=xe^squarerootx

    use product rule y=uv
    let u=x and v=e^squarerootx

    find du/dx and dv/dx and use product rule to find dy/dx

    once you have found dy/dx sub in x=4 and thus get your answer!
    Offline

    0
    ReputationRep:
    (Original post by generalebriety)
    "rt" = square root, I assume.

    I'm not talking about you, I'm talking about people like Decota who blatantly know better and are posting full solutions just to piss me off.
    lol not at all, I was just following suit of the other people in the thread, see I even gave a hint in my first post but then people started posting solutions ..
    • Wiki Support Team
    Offline

    14
    ReputationRep:
    Wiki Support Team
    (Original post by hi there)
    I did all of that, but the problem is when you put it altogether, whith one big messy equation which is hard to rearrange!
    As I said, post your working and we'll help you further. Or Decota will keep blatantly ruining the spirit of the forum. Whichever comes first, really. :rolleyes:
    • Wiki Support Team
    Offline

    14
    ReputationRep:
    Wiki Support Team
    (Original post by Decota)
    lol not at all, I was just following suit of the other people in the thread, see I even gave a hint in my first post but then people started posting solutions ..
    No one posted solutions apart from you.
    Offline

    2
    ReputationRep:
    (Original post by hi there)
    I did all of that, but the problem is when you put it altogether, whith one big messy equation which is hard to rearrange!
    What equation did you get? I will see if it corresponds with mine
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: July 13, 2007

University open days

  • Heriot-Watt University
    School of Textiles and Design Undergraduate
    Fri, 16 Nov '18
  • University of Roehampton
    All departments Undergraduate
    Sat, 17 Nov '18
  • Edge Hill University
    Faculty of Health and Social Care Undergraduate
    Sat, 17 Nov '18
Poll
Black Friday: Yay or Nay?
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

Equations

Best calculators for A level Maths

Tips on which model to get

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.