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    1. Can somebody please check if my final answers, methods & steps are correct?

      Find the set of values of x for which



      2) Solve the equation (give general solution as multiples of pi, in radian:



      3) Compute the integral [I used the formula : SinACosB = Sin(A+B) + Sin(A-B) A>B]:




      4) Find the general solution of theta:



      Thank you so much pals! If you are not able to verify all 4 questions, please feel free to check any one(s) that you can.

      Thank you again!

      Sid
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    (Original post by Sidhant Shivram)
    ...
    For first one, the quadratic inequality that you reach has additional constraints. Remember that the inequality sign changes when you multiply with a negative. Also, you evaluated the ranges incorrectly.
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    (Original post by Sidhant Shivram)
    1. [FONT=CMR12][SIZE=3]Can somebody please check if my final answers, methods & steps are correct...
    I don't think what you've said for the first question (about inequalities) is valid. Indeed, if a<b then ac<bc exactly when c is positive. If it is negative then the sign reverses. Therefore, given \frac{3n+4}{n-2} &lt; \frac{2n-1}{n-4} you can't just multiply by (n-2) say unless you know what the sign of that is.
    Here are some possible strategies:
    (i) Consider the cases -4&lt;n&lt;-2 etc. separately (a bit tedious) or
    (ii) Multiply by (n-2)^2(n-4)^2 and solve that. (Still a bit tedious, but less so)
    (iii) Assume EQUALITY holds, and then check each of the intervals afterwards.
    (iv) Use a graphical calculator, but ONLY if this is allowed; the examiner may not like this.
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    (Original post by lazy_fish)
    For first one, the quadratic inequality that you reach has additional constraints. Remember that the inequality sign changes when you multiply with a negative. Also, you evaluated the ranges incorrectly.
    (Original post by theOldBean)
    I don't think what you've said for the first question (about inequalities) is valid. Indeed, if a<b then ac<bc exactly when c is positive. If it is negative then the sign reverses. Therefore, given \frac{3n+4}{n-2} &lt; \frac{2n-1}{n-4} you can't just multiply by (n-2) say unless you know what the sign of that is.
    Here are some possible strategies:
    (i) Consider the cases -4&lt;n&lt;-2 etc. separately (a bit tedious) or
    (ii) Multiply by (n-2)^2(n-4)^2 and solve that. (Still a bit tedious, but less so)
    (iii) Assume EQUALITY holds, and then check each of the intervals afterwards.
    (iv) Use a graphical calculator, but ONLY if this is allowed; the examiner may not like this.
    Oh wait! Sorry! My plan was to multiply LHS & RHS with the square of the denominator (a positive number on both sides) and then proceed as usual. I shall post the edited version now. Thanks for pointing that out.
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    (Original post by lazy_fish)
    For first one, the quadratic inequality that you reach has additional constraints. Remember that the inequality sign changes when you multiply with a negative. Also, you evaluated the ranges incorrectly.
    (Original post by theOldBean)
    I don't think what you've said for the first question (about inequalities) is valid. Indeed, if a<b then ac<bc exactly when c is positive. If it is negative then the sign reverses. Therefore, given \frac{3n+4}{n-2} &lt; \frac{2n-1}{n-4} you can't just multiply by (n-2) say unless you know what the sign of that is.
    Here are some possible strategies:
    (i) Consider the cases -4&lt;n&lt;-2 etc. separately (a bit tedious) or
    (ii) Multiply by (n-2)^2(n-4)^2 and solve that. (Still a bit tedious, but less so)
    (iii) Assume EQUALITY holds, and then check each of the intervals afterwards.
    (iv) Use a graphical calculator, but ONLY if this is allowed; the examiner may not like this.
    Name:  ImageUploadedByTapatalk1420390394.142035.jpg
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    Better?

    Thanks again!


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    (Original post by Sidhant Shivram)
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    Yup.
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    (Original post by lazy_fish)
    Yup.
    Thanks!


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    (Original post by Sidhant Shivram)
    Name:  ImageUploadedByTapatalk1420390394.142035.jpg
Views: 96
Size:  234.7 KB

    Better?

    Thanks again!


    Sent from my iPhone using Tapatalk
    next time dont expand it just factor stuff out and expand the linear stuff inside which will give u the roots straight away. ie take it to one side and facto stuff to make it neater and much much quicker.


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    (Original post by physicsmaths)
    next time dont expand it just factor stuff out and expand the linear stuff inside which will give u the roots straight away. ie take it to one side and facto stuff to make it neater and much much quicker.


    Posted from TSR Mobile
    Oh yes! I see what you mean...Thanks!
 
 
 
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