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    Is there any way of checking a differential equation, maclaurin/taylor series on your calculator?
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    (Original post by Nikhilm)
    Is there any way of checking a differential equation, maclaurin/taylor series on your calculator?
    For series plug in a small value of x into both sides, like x=0.1
    And see if they are approximately the same
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    (Original post by Zacken)
    I feel bad for stealing the above question, so I'll contribute one:

    \displaystyle

\begin{equation*} \sum_{n=1}^m 2^n \tan (2^n \theta) \end{equation*}
    Spoiler:
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    Is it
    2\cot\2\theta - 2^{m+1}\cot\left({2^{m+1}\theta}  \right)?
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    (Original post by A Slice of Pi)
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    Is it
    2\cot\2\theta - 2^{m+1}\cot\left({2^{m+1}\theta}  \right)?
    :yes:
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    (Original post by Zacken)
    :yes:
    Very nice question! On most FP2 papers they tend to give you the identity first which I guess takes the fun out of it a little aha
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    (Original post by A Slice of Pi)
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    Is it
    2\cot\2\theta - 2^{m+1}\cot\left({2^{m+1}\theta}  \right)?
    Surely there is some hint to this question??
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    (Original post by A Slice of Pi)
    Very nice question! On most FP2 papers they tend to give you the identity first which I guess takes the fun out of it a little aha
    Thanks! I just took the idea from yours and packaged it into a slightly different trig form. :lol:
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    (Original post by fpmaniac)
    Can anyone help me with a few questions:

    1a. Find the value of z which satisfies both |z+2| = |2z-1| and arg z = pi/4
    b. Hence shade in the region R on an Argand diagram which satisfies both |z+2| ≥ |2z-1| and pi/4≤arg≤ pi

    2. Given that |z+1-i| = 1 find the greatest and least values of |z-1|
    3. Find the ccartesian equation of the locus of z when z-z* = 0 ...... what does the star mean
    Question 1 looks to be 'death by diagram' Drawing the Argand diagram, with the locus of z (it divides the line joining -2 and 1/2 on the real axis in the ratio 2:1) and use trig to figure out the position of z.
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    (Original post by Pyslocke)
    Surely there is some hint to this question??
    Nope. But if you're ever stuck on a series question in FP2 then there's a 90% chance it's going to be method of differences.
    Spoiler:
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    (The remaining 10% of sums may come from complex numbers like cos x + cos 2x + cos 3x + ..., but this hardly ever comes up) You can actually even use MOD on this too.
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    (Original post by A Slice of Pi)
    Nope. But if you're ever stuck on a series question in FP2 then there's a 90% chance it's going to be method of differences.
    Spoiler:
    Show
    (The remaining 10% of sums may come from complex numbers like cos x + cos 2x + cos 3x + ..., but this hardly ever comes up) You can actually even use MOD on this too.
    I'm not stuck trying to figure out whether to use method of differences, but how to find a trig identity that I can actually use just from that. What paper was this btw?
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    (Original post by Pyslocke)
    I'm not stuck trying to figure out whether to use method of differences, but how to find a trig identity that I can actually use just from that. What paper was this btw?
    It's not from a particular paper it's just a question for practice or a challenge. You'd almost certainly be given a suitable identity in the FP2 exam (and there are probably a few suitable identities out there).
    Hint:
    Spoiler:
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    \displaystyle\frac{d}{d x}\ln | \sec x | = \tan x
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    (Original post by A Slice of Pi)
    Spoiler:
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    Is it
    2\cot\2\theta - 2^{m+1}\cot\left({2^{m+1}\theta}  \right)?
    Did you sin and cos double angle formulae?
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    (Original post by A Slice of Pi)
    Question 1 looks to be 'death by diagram' Drawing the Argand diagram, with the locus of z (it divides the line joining -2 and 1/2 on the real axis in the ratio 2:1) and use trig to figure out the position of z.
    So its a perpendicuar bisector for x = 2 and x = 0.5. How do you use trig? What do you do with the arg z = pi/4 bit. Or do you mean first find the equation for |z| bit then equal that to the equation of arg.
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    (Original post by edothero)
    For series plug in a small value of x into both sides, like x=0.1
    And see if they are approximately the same
    You can't do that for a dy/dx expansion though right?
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    (Original post by fpmaniac)
    So its a perpendicuar bisector for x = 2 and x = 0.5. How do you use trig? What do you do with the arg z = pi/4 bit. Or do you mean first find the equation for |z| bit then equal that to the equation of arg.
    Having just looked at it again, I don't think it will be a straight line at all, but rather a circle. Put z = x + iy into that locus and then get it into Cartesian form.
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    (Original post by Nikhilm)
    Did you sin and cos double angle formulae?
    Yes
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    You know when the PI is dodgy and is part of the CF then do we always mutliply that value of the PI, by x?

    And how come we do thids
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    Do we need to know FP1 Proof by Induction, Newton Raphson, Matrices, C4 Vectors, itinerary formula etc for FP2?
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    (Original post by TheFarmerLad)
    Do we need to know FP1 Proof by Induction, Newton Raphson, Matrices, C4 Vectors, itinerary formula etc for FP2?
    I think once they asked you to prove De Movire's theorem by induction, but I'm not certain.
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    (Original post by A Slice of Pi)
    I think once they asked you to prove De Movire's theorem by induction, but I'm not certain.
    Hate proof by induction
 
 
 
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