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## Homework Statement

For all [itex]x\in R[/itex] , [itex]f(x)>0[/itex] . Using precise definition of limits and infinite limits, prove that [itex]\lim_{x\to a}f(x)=\infty[/itex] if and only if [itex]\lim_{x\to a}\frac{1}{f(x)}=0 [/itex]

## Homework Equations

## The Attempt at a Solution

I know the precise definition of limits and infinite limits but I cannot see how they can be applied in this case. Also this is biconditional statement so I guess I gotta deduce 2 sub-proofs before drawing the conclusion. Ok that's all I've thought of this far, any hints would be greatly appreciated, thanks!