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## Homework Statement

Given is: f is a function that maps D onto the Real numbers, and c is within D and it is a limit point, and f(x) =/= 0 for all x in D, and [itex]\lim_{x \to c} f(x) = \infty[/itex]

I have to proof that:

[itex]\lim_{x \to c} \frac{1}{f(x)} = 0[/itex]

## The Attempt at a Solution

This means that according to the definition I have to proof that [itex]\forall \epsilon \ \exists \delta[/itex] so that [itex] \forall x \in D \ with \ 0 < |x-c|< \delta \ \ : |\frac{1}{f(x)} - 0|< \epsilon [/itex].

Im not sure how to go on from here. Or do i have to do something else?