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

Primary tabs

Lesson Parent: 
Function Limits IX: Horizontal Asymptotes And The Limit Of $f(x)$ As $x$ Tends To Infinity
Problem: 

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

Answer: 

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

SAMPLE SOLUTION

All of our problems have fully worked out, logical solutions. We connect every solution to its underlying lesson so you can understand the concepts needed to solve any problem and reinforce your learning by practicing with similar problems. All of the formulas are available to our subscribers, but here is a sample of the problem solution you will see when you log in:



Solution: 

Recall that we need to show for every <Sign in to see all the formulas> there exists a $Y$ such that when <Sign in to see all the formulas> then <Sign in to see all the formulas>. In this particular problem $f(x)$ is a constant so that <Sign in to see all the formulas> and the limit is $C$. So with <Sign in to see all the formulas> and $L=C$ we automatically have <Sign in to see all the formulas>. So we can pick any $Y$ and and when <Sign in to see all the formulas> then <Sign in to see all the formulas>. Therefore,

<Sign in to see all the formulas>