a. Consider d on R, the real line, to be d(x,y) = |x2 – y2|. Show...

a. Consider d on R, the real line, to be d(x,y) = |x² – y²|. Show that d is NOT a metric on R. b.Consider d on R, the real line, to be d(x,y) = |x³ – y³|. Show that d is a metric on R.

2. Let d on R be d(x,y) = |x-y|. The “usual” distance. Show the interval (-2,7) is an open set.

Note: you must show that any point z in the interval has a ball centered at z, and that ball is completely contained within the interval (-2,7).

Expert Solution

Colby Messinger answered 1 year ago

Given the set A = {(x, y) ∈ R2 | x2 + y2 < 1 and...

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f(r,?) f(x,y) r(cos(?)) = x r(cos(2?)) = ? r(cos(3?)) = x3-3xy2/x2+y2 r(cos(4?)) = ? r(cos(5?)) =...

f(r,?) f(x,y) r(cos(?)) = x r(cos(2?)) = ? r(cos(3?)) = x3-3xy2/x2+y2 r(cos(4?)) = ? r(cos(5?)) = ? Please complete this table. I am having trouble converting functions from polar to cartesian in the three dimensional plane. I understand that x=rcos(?) and y=rsin(?) and r2 = x2 + y2 , but I am having trouble understanding how to apply these functions.

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