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  • Perplex
    IB Math AAHL
    /
    Transformations & asymptotes
    /

    Problem Bank

    [Maximum mark: 19]

    Consider the relation ​(ax​)n+(by​)n=1​ for positive constants ​a​ and ​b​ and positive even integer ​n. The graph of the relation is drawn below for ​a>b​ and ​n=2,3​ and ​4.


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    1. Give an expression for ​dxdy​​ in terms of ​a,b​ and ​n.

      [5]

      To earn a crown, get your answer ready before you reveal the options!

    2. Evaluate the limit ​n→∞lim​dxdy​​ in the case where ​∣∣∣∣​yx​∣∣∣∣​​ is

      (i)

      1. greater than ​ba​​

        [2]
      2. less than ​ba​​

        [2]
      3. equal to ​ba​​

        [2]

    The graph of ​(ax​)2n+(by​)2n=1​ encloses a region of area of ​A.

    1. Given an expression for ​n→∞lim​A​ in terms of ​a​ and ​b.

      [3]
    2. Find the oblique asymptote of the graph of ​(ax​)5+(by​)5=1.

      [5]

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