Prove that \begin{equation}\lim_{x\to 2}\,2x-1=3.\end{equation}

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Lesson Parent: 
Function Limits III: The Gory Details
Problem: 

Prove that \begin{equation}\lim_{x\to 2}\,2x-1=3.\end{equation}

Answer: 

It is true that \begin{equation}\lim_{x\to 2}\,2x-1=3.\end{equation}

SAMPLE SOLUTION

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Solution: 

Here are the general set of steps we need to take to do our proof.

Notice that this is the limit of a straight line. See this for the general solution to these type of problems.