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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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Give an expression for dxdy in terms of a,b and n.
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Evaluate the limit n→∞limdxdy in the case where ∣∣∣∣yx∣∣∣∣ is
(i)
greater than ba
less than ba
equal to ba
The graph of (ax)2n+(by)2n=1 encloses a region of area of A.
Given an expression for n→∞limA in terms of a and b.
Find the oblique asymptote of the graph of (ax)5+(by)5=1.
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