Integration

Maths and statistics discussion, revision, exam and homework help.

Announcements Posted on
TSR launches Learn Together! - Our new subscription to help improve your learning 16-05-2013
IMPORTANT: You must wait until midnight (morning exams)/4.30AM (afternoon exams) to discuss Edexcel exams and until 1pm/6pm the following day for STEP and IB exams. Please read before posting, including for rules for practical and oral exams. 28-04-2013
Search Thread
Advanced Search
Sign in to Reply
  1. King-Panther's Avatar
    61 03-04-2012  18:03
    • Vengeful, Imperial Overlord of The Student Room
    • Location: London
    • Posts: 3,710
    Re: Integration
    (Original post by raheem94)
    For question 26,
    \displaystyle 2^{3x+1}=4^{x}
    Take log of both sides,
    \displaystyle log\left(2^{3x+1}\right)=log \left(4^{x}\right) \implies (3x+1)log2=xlog4
    So, (3x+1)log2 = xlog4

    (3x+1) =xlog4/log2

    3x+1=2

    3x = 1

    x = 1/3

    ??? which isn't right
  2. King-Panther's Avatar
    62 03-04-2012  18:05
    • Vengeful, Imperial Overlord of The Student Room
    • Location: London
    • Posts: 3,710
    Re: Integration
    (Original post by raheem94)
    \displaystyle log\left(\frac{2x^2}{x^3}\right) \implies log\left(\frac2{x}\right)
    So what does x = 2?
  3. raheem94's Avatar
    63 03-04-2012  18:12
    • TSR Demigod
    • Posts: 5,512
    Re: Integration
    (Original post by King-Panther)
    So, (3x+1)log2 = xlog4

    (3x+1) =xlog4/log2

    3x+1=2

    3x = 1

    x = 1/3

    ??? which isn't right
    (3x+1) =xlog4/log2
    3x+1=2x

    You missed out the 'x'.
  4. raheem94's Avatar
    64 03-04-2012  18:14
    • TSR Demigod
    • Posts: 5,512
    Re: Integration
    (Original post by King-Panther)
    So what does x = 2?
    According to the question,
    \displaystyle log\left(\frac2{x}\right) = log0.5

    Remove logs,
    \displaystyle \frac2{x}= 0.5
  5. Zuzuzu's Avatar
    65 03-04-2012  18:15
    • Peer Of The TSR Realm
    • Posts: 1,540
    Re: Integration
    (Original post by just george)
    24. yes it is true, the first wiki image steve2005 put up states that if f''(x)<0 then f has a local maximum at x.
    i.e. if the second derivative of f(x) is less than 0 (negative), there is a local maximum.
    So clearly all local maximum points will produce a negative second derivative
    Consider f(x) = -x^{64}.
  6. King-Panther's Avatar
    66 03-04-2012  19:08
    • Vengeful, Imperial Overlord of The Student Room
    • Location: London
    • Posts: 3,710
    Re: Integration
    (Original post by raheem94)
    According to the question,
    \displaystyle log\left(\frac2{x}\right) = log0.5

    Remove logs,
    \displaystyle \frac2{x}= 0.5
    therefore x =2/0.5

    x = 1???

    I take I substitute value of x into the equation to get log(0.5)
  7. raheem94's Avatar
    67 03-04-2012  19:09
    • TSR Demigod
    • Posts: 5,512
    Re: Integration
    (Original post by King-Panther)
    therefore x =2/0.5

    x = 1???

    I take I substitute value of x into the equation to get log(0.5)
    2/0.5=4 not 1
  8. King-Panther's Avatar
    68 03-04-2012  19:15
    • Vengeful, Imperial Overlord of The Student Room
    • Location: London
    • Posts: 3,710
    Re: Integration
    (Original post by raheem94)
    2/0.5=4 not 1
    2/x = 0.5, if you make x the subject, you multiply 2 by .5 ....


    When I sub 4 into the equation logx+log2x+logx^3 i dont get 0.5
  9. Brit_Miller's Avatar
    69 03-04-2012  19:22
    • Benevolent Member
    • Location: Bristol
    • Posts: 683
    Re: Integration
    (Original post by King-Panther)
    2/x = 0.5, if you make x the subject, you multiply 2 by .5 ....
    No, you'd multiply through by x, then divide through by 0.5, so it does equal 4.
  10. King-Panther's Avatar
    70 03-04-2012  19:36
    • Vengeful, Imperial Overlord of The Student Room
    • Location: London
    • Posts: 3,710
    Re: Integration
    (Original post by Brit_Miller)
    No, you'd multiply through by x, then divide through by 0.5, so it does equal 4.
    of course, however, when i sub 4 into the equation i dont get 0.5
  11. King-Panther's Avatar
    71 03-04-2012  19:37
    • Vengeful, Imperial Overlord of The Student Room
    • Location: London
    • Posts: 3,710
    Re: Integration
    (Original post by Brit_Miller)
    No, you'd multiply through by x, then divide through by 0.5, so it does equal 4.
    for Q)31, i got 8
  12. raheem94's Avatar
    72 03-04-2012  19:41
    • TSR Demigod
    • Posts: 5,512
    Re: Integration
    (Original post by King-Panther)
    2/x = 0.5, if you make x the subject, you multiply 2 by .5 ....


    When I sub 4 into the equation logx+log2x+logx^3 i dont get 0.5
    \displaystyle \frac{2}{x} = 0.5 \implies \frac{2}{x} = \frac12 \implies x \times \frac2{x} = x \times \frac12 \implies 2 = \frac{x}{2} \implies 2 \times 2 = 2\times \frac{x}2 \implies 4=x

    Your equation was, \displaystyle logx+log2x-logx^3 =log0.5
    \displaystyle log0.5=-0.301...
    \displaystyle log4+log2(4)-log4^3=log4+log8-log64=-0.301...
  13. just george's Avatar
    73 03-04-2012  19:42
    • Exalted Member
    • Posts: 357
    Re: Integration
    (Original post by Zuzuzu)
    Consider f(x) = -x^{64}.
    f'(x)=-64x^6^3

    so turning point at x=0

    f''(x)=-4032x^6^2

    so at x=0, f''(x)=0

    so not a maximum..?

    i dont understand what you're trying to say? is what i said incorrect? :L
  14. King-Panther's Avatar
    74 03-04-2012  19:48
    • Vengeful, Imperial Overlord of The Student Room
    • Location: London
    • Posts: 3,710
    Re: Integration
    (Original post by raheem94)
    \displaystyle \frac{2}{x} = 0.5 \implies \frac{2}{x} = \frac12 \implies x \times \frac2{x} = x \times \frac12 \implies 2 = \frac{x}{2} \implies 2 \times 2 = 2\times \frac{x}2 \implies 4=x

    Your equation was, \displaystyle logx+log2x-logx^3 =log0.5
    \displaystyle log0.5=-0.301...
    \displaystyle log4+log2(4)-log4^3=log4+log8-log64=-0.301...
    ahhhh

    :hugs:
  15. King-Panther's Avatar
    75 03-04-2012  19:50
    • Vengeful, Imperial Overlord of The Student Room
    • Location: London
    • Posts: 3,710
    Re: Integration
    (Original post by raheem94)
    \displaystyle \frac{2}{x} = 0.5 \implies \frac{2}{x} = \frac12 \implies x \times \frac2{x} = x \times \frac12 \implies 2 = \frac{x}{2} \implies 2 \times 2 = 2\times \frac{x}2 \implies 4=x

    Your equation was, \displaystyle logx+log2x-logx^3 =log0.5
    \displaystyle log0.5=-0.301...
    \displaystyle log4+log2(4)-log4^3=log4+log8-log64=-0.301...
    Q)31 i got 8

    also, for 33, what do i do when 3/2x^2, do i multiply 3 by 2x^2 do its 6x^-2
    Last edited by King-Panther; 03-04-2012 at 19:59.
  16. just george's Avatar
    76 03-04-2012  19:55
    • Exalted Member
    • Posts: 357
    Re: Integration
    and for (26) couldnt you just do?

    2^{3x+1} = 4^x

    2^{3x+1} = (2\times2)^x

    2^{3x+1} = 2^x\times2^x

    2^{3x+1} = 2^{2x}

    3x+1 = 2x

    x = -1

    Guess if your happy with laws of logs and things either way is fine, dont know why i chose to do it this way
  17. King-Panther's Avatar
    77 03-04-2012  19:59
    • Vengeful, Imperial Overlord of The Student Room
    • Location: London
    • Posts: 3,710
    Re: Integration
    (Original post by just george)
    and for (26) couldnt you just do?

    2^{3x+1} = 4^x

    2^{3x+1} = (2\times2)^x

    2^{3x+1} = 2^x\times2^x

    2^{3x+1} = 2^{2x}

    3x+1 = 2x

    x = -1

    Guess if your happy with laws of logs and things either way is fine, dont know why i chose to do it this way
    indeed i could have, thanks.... for 31 is it 8?
  18. just george's Avatar
    78 03-04-2012  20:00
    • Exalted Member
    • Posts: 357
    Re: Integration
    (Original post by King-Panther)
    indeed i could have, thanks.... for 31 is it 8?
    yes, whats the relevance of your answer though?

    edit:
    (Original post by King-Panther)
    also, for 33, what do i do when 3/2x^2, do i multiply 3 by 2x^2 do its 6x^-2
    what do you mean? you have \frac{3}{2}x^2 , so to differentiate it you times it by the power, and then take one off the power?
    Last edited by just george; 03-04-2012 at 20:03.
  19. King-Panther's Avatar
    79 03-04-2012  20:11
    • Vengeful, Imperial Overlord of The Student Room
    • Location: London
    • Posts: 3,710
    Re: Integration
    (Original post by just george)
    yes, whats the relevance of your answer though?
    Dy/dx tells us what the gradient is when we at x when we sub it in, d2y/dx2 tells us in which direction its going, its a positive number so its a minimum going in the positive direction?
  20. King-Panther's Avatar
    80 03-04-2012  20:14
    • Vengeful, Imperial Overlord of The Student Room
    • Location: London
    • Posts: 3,710
    Re: Integration
    (Original post by just george)
    yes, whats the relevance of your answer though?

    edit:


    what do you mean? you have \frac{3}{2}x^2 , so to differentiate it you times it by the power, and then take one off the power?
    No, the fraction is \frac{3}{2x^2}
    Last edited by King-Panther; 03-04-2012 at 20:16.
Sign in to Reply
Search Thread
Advanced Search
Share this discussion:  
Useful resources

Articles:

Study Help rules and posting guidelinesStudy Help Member of the Month nominationsGuide to MathematicsMathematics resourcesMathematics websitesMathematics revision notes in the TSR wikiCambridge Assessment admissions tests (including STEP)How to use LaTeXCareers in Mathematics

Useful Dates:

Quick Link:

Unanswered Maths Threads

Groups associated with this forum:

View associated groups
Article updates
Moderators

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

This forum is moderated by:

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

Shortcuts

Get Started

TSR Group

Using TSR

Info

Connect with TSR

Reputation gems:
The Reputation gems seen here indicate how well reputed the user is, red gem indicate negative reputation and green indicates a good rep.
Post rating score:
These scores show if a post has been positively or negatively rated by our members.