For all except one of the mentioned statements implies that limx4 F(x) = . For each statement,

For all except one of the mentioned statements implies that limx→4 F(x) = π.

For each statement, explain either why it implies that limx→4 F(x) = π or provide an example of a function F for which the statement is true, yet limx→4 F(x) = π fails.

(a) For every a > 0 there is some b > 0 such that |F(δ) − π| < a for all δ such that 0 < |δ − 4| < b.

(b) For every ι > 0 there is some δ > 0 such that |F(w) − π| < ι for all w such that 0 < |w − 4| < δ.

(c) There is some δ > 0 such that |F(x) − π| < ϵ for all ϵ > 0 and all x such that 0 < |x − 4| < δ.

(d) There is ϵ > 0 and δ > 0 such that |F(x) − π| < ϵ whenever 0 < |x − 4| < δ.

(e) For every ϵ there is some δ > 0 such that |F(x) − π| < ϵ whenever 0 < |x − 4| < δ.

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