Question

Given f(x)=1/x, find a number delta such that:

if |x-2| < delta then |(1/x)-.5| < .2

Answer 1

BODMAS don't ring any bells

Answer 2

|(1/x) - 1/2| < 2/10
-2/10 < (1/x) - (1/2) < 2/10
-2x/10 < 1 - x/2 < 2x/10
-x/5 < 1 - x/2 < x/5
-2x/5 < 2 - x < 2x/5
|2 - x| < 2x/5 = delta

So with delta = 2x/5 then if |x -2| < delta then |(1/x) - .5| < .2

Answer 3

the answer in the book says 4/7 or something smaller. Explain