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

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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.

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>