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    I am destined to fail! lol.

    Anyhow the question is from the exam style paper in the back of the C3 edexcel book for anyone who has it

    f(x)=e^2x-1
    The Curve C with equation y=f(x) meets the y-axis at P
    The tangent to C at P crosses the x-axis at Q

    a) find, to 3 decimal places, the area of triangle POQ where O is the origin

    The line y=2 intersects C at the point R

    b) find the exact value of the x-coordinate of R
    Now I dont remember being taught anything like this lol.
    Any help would be great thanks
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    Could you clarify what f(x) is? Is it e^{2x}-1 or e^{2x-1} or something else?
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    its the second one.
    sorry Im unsure how to type it like that.. (if anyone would like to point me in the right direction!)
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    I'd like to know how to work out the area too, so if anyone can do this please explain?
    I haven't been taught this either. OP is this question from the new edexcel heinman book? if yes, can you tell which page?
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    This type of question is often easier if you sketch out the graph with a diagram. First, you need to find f'(x) by differentiating. Then you can find where P is by evaluating f(0), since P will be the point on the line C where x=0.

    Now find f'(0) which will be the gradient of your tangent. Since your tangent will be a straight line, you can find its equation in the form y=mx+c where m=f'(0) and c=f(0).

    Now you have the equation for the tangent, set y=0 for it to find where it crosses the x axis. This will give you the point Q.

    Now draw all of this on your diagram. You should see that POQ is a right angled triangle, where you can find the area using 1/2 * base * height.

    For part b, you need to solve e^{2x-1}=2 for x by taking logs.

    To make equations look the way I made them, there are instructions on http://www.thestudentroom.co.uk/wiki/LaTeX
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    (Original post by Remarqable M)
    I'd like to know how to work out the area too, so if anyone can do this please explain?
    I haven't been taught this either. OP is this question from the new edexcel heinman book? if yes, can you tell which page?
    hiya.. yeh its from the heinemann book. its the exam style paper at the back of the book after the differentiation topic. Its page 139.
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    ok, you know the co-ordinates of P, since x = 0 and you have the formula y = f(x) to find y.
    Differentiate f and evaluate at P to find the gradient of C at P. With this, you have a co-ordinate and a gradient, so you should able to easily find the equation of the straight line and use it to find the x-value of Q (where y=0). It should be pretty easy to find the area from here
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    i havent started c3 yet but i couldnt resist this.
    to find P substitute for when x=0 that should give u the point (0,0.368)
    to find q find the equation of the tangent at p and substitute for when y=0 that should be (2,0)
    the area is then (2*0.368)/2 which is also 0.368(the tri.POQ is perpendicular at origin)
    i hope i'm right.
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    (a) C meets y-axis where x=0
    ⇒ y=e^(−1)
    Find gradient of curve at P.

    dy/dx =2e^(2x−1)

    At x=0, dy/dx =2e^(−1)

    Equation of tangent is y−e^(−1)=2e^(−1)x

    This meets x-axis at Q, where y=0
    ⇒ Q≡(-1/2, 0)

    Area of △POQ=1/2 x 1/2 x e^(-1)=1/4e^(-1)=0.092

    (b) At R, y=2 ⇒ 2=e^(2x−1)
    ⇒ 2x−1=ln2
    ⇒ 2x=1+ln2
    ⇒ x=1/2 x (1+ln2)

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    (Original post by beckaboos.)
    sorry Im unsure how to type it like that.. (if anyone would like to point me in the right direction!)
    how about;
    e^(2x+1)
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    Thank you everyone for your replies it makes so much more sense now. Thats one to tick off my revision oh not a clue checklist!
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    (Original post by obviouslystudying)
    how about;
    e^(2x+1)
    After I wrote that I did think I could of written it like that
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    Alternatively you could use Latex
 
 
 
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Updated: January 17, 2010

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