I'm sure this is a really simple problem, I just wanted to make sure that I'm doing this correctly.

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Suppose that \rightarrow R" alt="f \rightarrow R" /> has a limit at . Prove that \rightarrow R" alt="|f| \rightarrow R" /> has a limit at and that .

Proof: Let . Then, such that, if . By the Inverse Triangle Inequality, we have that . Therefore, .