(See) Let f: D \rightarrow R . Mark each statement True or False. Justify each answer. In the definition of uniform continuity, the positive δ depends

Question: Let $f: \mathrm{D} \rightarrow \mathbb{R} .$ Mark each statement True or False. Justify each answer.

In the definition of uniform continuity, the positive $\delta$ depends only on the function $f$ and the given $\varepsilon>0$.
If $f$ is continuous and $\left(x_{n}\right)$ is a Cauchy sequence in $D$, then $\left(f\left(x_{n}\right)\right)$ is
a Cauchy sequence.
If $f:(a, b) \rightarrow \mathbb{R}$ can be extended to a function that is continuous on [a, b], then $f$ is uniformly continuous on $(a, b)$.

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(See) Let f: D \rightarrow R . Mark each statement True or False. Justify each answer. In the definition of uniform continuity, the positive δ depends

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