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    (Original post by iAmanze)
    is irrational

    How would I go about proving that. I can do it for square of 2 but not 3.
    This proof is slightly harder. Start the same as the proof for the irrationality of \sqrt2, but consider the oddness/evenness of the numbers.
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    (Original post by Alevelstudent678)
    I never know what rule to use when you integrating/differentiating any tips?
    chain rule when integrating by parts
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    (Original post by ArielHaeems)
    Some notes:

    -Odd functions: f(-x) = -f(x) and these functions show rotational symmetry about the origin, order 2
    -Even functions: f(x) = f(-x) and these functions show symmetry across the y-axis
    -Reflecting f(x) across y=x gives f^-1(x) (the inverse function)
    -The domain of f(x) is the range of f^-1(x), and vice versa
    -If the gradient of f(x) at (x,y) is a, then the gradient of f^-1(x) at (y,x) is 1/a

    -Differentiating: sin(x) --> cos(x) --> -sin(x) --> -cos(x) --> sin(x)...
    -Differentiating sin(ax) gives acos(ax)

    -Integrating e^x gives e^x
    -Integrating f'(x)/f(x) gives ln(f(x))
    -integrating e^ax gives (1/a)e^ax
    -Integrating sin(ax) gives -(1/a)cos(ax)
    -Integration by parts formula: uv - (Integral of)vdu
    -Indefinite integrations introduce +c as an unknown value
    Actually \displaystyle \int \frac{f'(x)}{f(x)}=ln|f(x)|+C.

    Don't forget the modulus signs.

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    What's the hardest paper you've all done up to yet?


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    Jan 11 is pretty challenging

    _Caz_
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    (Original post by _Caz_)
    What's the hardest paper you've all done up to yet?


    Posted from TSR Mobile
    june 2015
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    (Original post by genius10)
    june 2015
    Don't jinx it
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    Can someone explain Sweezy's oligopoly theory to me?

    SORRY, got the econ thread open on the other tab !
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    (Original post by HenryHein)
    Can someone explain Sweezy's oligopoly theory to me?
    yh lad, simple.
    see wee man if ye have 12 eggs and differntiate by simon cowels ego you get the product of the two masses between them divided by the distance between the egs squared. I AINT NO HEAVY DUTY BEVVY MERHCANT BUT EVEN I KNOW THAT LADDIE
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    (Original post by HenryHein)
    Can someone explain Sweezy's oligopoly theory to me?

    SORRY, got the econ thread open on the other tab !
    :ahee::ahee::ahee:
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    (Original post by genius10)
    june 2015
    haha
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    (Original post by Robbo54)
    Jan 11 is pretty challenging

    _Caz_
    Might have a go of that one then. Nothing like struggling through a hard paper to get your confidence up haha. thanks
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    Hype.

    Posted from TSR Mobile
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    Hey I wonder if anyone could help me: when combining transformations and you have two transformations that affect x or two that affect y do you always do the stretch before the translation?
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    (Original post by _Caz_)
    Hey I wonder if anyone could help me: when combining transformations and you have two transformations that affect x or two that affect y do you always do the stretch before the translation?
    That's a good question. I believe it is enlargement first, translation second.
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    If you're asked to differentiate something but it isn't y= then how do you write your answer?
    d/dx or do you just write you answer because I want to make it clear what my final answer is
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    (Original post by _Caz_)
    Hey I wonder if anyone could help me: when combining transformations and you have two transformations that affect x or two that affect y do you always do the stretch before the translation?
    In some cases it doesn't matter, in other cases it does matter. It depends on the function and the transformations.
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    (Original post by lizard54142)
    For translation and stretch combinations the order doesn't matter.
    Now I'm confused...say you have the transformation 2f(x) + 1, and the point, (0,1).

    If you do enlargement and then translation, 0 becomes 1, and 1 becomes 3.

    But if you do translation and then enlargement, 0 becomes 2 and 1 becomes 4?

    pls help

    EDIT: enlargement isn't multiplication, I think that's what it is
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    (Original post by AlexParmenter)
    If you're asked to differentiate something but it isn't y= then how do you write your answer?
    d/dx or do you just write you answer because I want to make it clear what my final answer is
    could you give an example?
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    (Original post by ArielHaeems)
    could you give an example?
    Name:  image.jpg
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    Edit: nevermind the marksheme sets it equal to y then used dy/dx
    Thanks anyway
 
 
 
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