Prove that \begin{equation}\lim_{x\to a}\,K=K\end{equation} where $K$ is a constant.

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

Prove that \begin{equation}\lim_{x\to a}\,K=K\end{equation} where $K$ is a constant.

Answer: 

It is true that \begin{equation}\lim_{x\to a}\,K=K\end{equation} where $K$ is a constant.

SAMPLE SOLUTION

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Solution: 

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

Here are the steps for this problem:

Step Description
1 We make the guess that <Sign in to see all the formulas> can be any real number $R$. We say that <Sign in to see all the formulas>.
2 Say <Sign in to see all the formulas>.
3 <Sign in to see all the formulas>
4 Now assume that we are at some value for $x$ such that <Sign in to see all the formulas>.
5 Now plug the function <Sign in to see all the formulas> into <Sign in to see all the formulas> so that we have <Sign in to see all the formulas>.
6 We don't need to do any algebra since <Sign in to see all the formulas> given any value of <Sign in to see all the formulas>.
7 Since $C$ is arbitrary we have a <Sign in to see all the formulas> such that <Sign in to see all the formulas>.