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Mathematics
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1 Oct 2019

In the following relation between two quantities which relation has exactly one output for each input?

  1. y2=2x

  2. y2=9-x2

  3. y= x

   d. y=x2-1

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Irving Heathcote
Irving HeathcoteLv2
5 Jul 2019
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Related questions

why is "x − y is a rational number" is not antisymmetric while "x = 2y" is antisymmetric

the proof I found for the first one is that "Since (1, −1) and (−1, 1) are both in R,
the relation is not antisymmetric." While the proof for the other was, "To see that it is antisymmetric, suppose that x = 2y, and y = 2x. Then y = 4y, from
which it follows that y = 0 and hence x = 0. Thus the only time that (x, y) and (y, x) are both in R
is when x = y (and both are 0)".
now the question is, why is it enough for the first equation to give an example that lies outside the relation to proving that it is NOT antisymmetric. Whereas for the second equation it was enough to give one example to prove that it is antisymmetric, even though in the relation R there exists element which is not antisymmetric

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1. (30 pts) (I) Calculate the derivatives of the following functions. NO NEED TO SIMLIFY ! (a) (8 pts) y = x tan-1 (x5) (b) (8 pts) y = xsin x (II) (14 pts) The curve with equation is a "rotated ellipse". x2 + xy + y2 = 4 (a) Use implicit differentiation to find the derivative (b) Consider the two points (3, -1) and (2, -2). Show that one of these points lies on the ellipse defined above, and one does not. (c) For the point in part (b) which lies on the ellipse, find the equation of the line tangent to the ellipse at this point.

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