http://gyazo.com/4979f938842fc56762a4cd166d33e10b

Lim f(x) = 0 as x -> ∞

When x > n_{0 } then f(x) < small number epsilon . If we take this as .0000001, it is true that f(x) < 0.00000001

For example let us take f(x)=1/x

If x > 1/0.00000001 =10^{8} > 100 million, then f(x) < 0.00000001

First statement is true

The limit will be approached but not attained.

Hence there is no finite x for which f(x) =0

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