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Limit of $x^2$ with a discontinuity at $x=3$ .

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Lesson Parent:

Problem:

What is
$\begin{equation} \lim_{x\to 3}\,f(x) \end{equation}$
where
$\begin{equation} f(x)=\left\{ \begin{array}{r@{\quad\quad}l} x^2, & x\lt 3\\ 1, & x=3\\ x^2, & x>3\\ \end{array} \right. . \end{equation}$

Answer:

9

Solution:

We know that

<Sign in to see all the formulas>

This means that when <Sign in to see all the formulas> then <Sign in to see all the formulas>. Recall that <Sign in to see all the formulas> means that <Sign in to see all the formulas>. Since we assume that <Sign in to see all the formulas>, we don't need to know what $f(3)$ is. In this problem, <Sign in to see all the formulas>, but it could be any other number or not even defined at all! For example,

<Sign in to see all the formulas>

The function

$g(x)$ is not even defined at

$x=3$ .

Limit of x2x^2 with a discontinuity at x=3x=3.

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SAMPLE SOLUTION

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GAIN AN ADVANTAGE

Limit of $x^2$ with a discontinuity at $x=3$ .