SOLUTION: prove: if t>0, there exists b such that if x>b then (1/(sqrt(x))) < t

SOLUTION: prove: if t>0, there exists b such that if x>b then (1/(sqrt(x))) < t

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Question 361025: prove: if t>0, there exists b such that if x>b then (1/(sqrt(x))) < t
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Let .
Proof:
If, then because b < x, .
, since t>0.
, after transposition and factoring the quadratic expression on the right.
, after dividing both sides by , which is surely positive. So
,and thus
, since is positive.
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