Solution Found!
Let a. Find and b. Does exist? If so, what is it? If not,
Chapter 2, Problem 3E(choose chapter or problem)
\(f(x)=\left\{\begin{array}{l}3-x, x<2 \\\frac{x}{2}+1, x>2\end{array}\right.\)
a. Find \(\lim _{x \rightarrow 2^{+}} f(x)\) and \(\lim _{x \rightarrow 2^{-}} f(x)\).
b. Does \(\lim _{x \rightarrow 2} f(x)\) exist? If so, what is it? If not, why not?
c. Find \(\lim _{x \rightarrow 4^{-}} f(x)\) and \(\lim _{x \rightarrow 4^{+}} f(x)\).
d. Does \(\lim _{x \rightarrow 4} f(x)\) exist? If so, what is it? If not, why not?
Equation Transcription:
{
Text Transcription:
f(x)= {x/2+1, x >2 3-x x<2
Lim_x right arrow 2^+f(x)
Lim_x right arrow 2^-f(x)
Lim_x right arrow 2^f(x)
Lim_x right arrow 4^-f(x)
Lim_x right arrow 4^+f(x)
Lim_x right arrow 4f(x)
Questions & Answers
QUESTION:
\(f(x)=\left\{\begin{array}{l}3-x, x<2 \\\frac{x}{2}+1, x>2\end{array}\right.\)
a. Find \(\lim _{x \rightarrow 2^{+}} f(x)\) and \(\lim _{x \rightarrow 2^{-}} f(x)\).
b. Does \(\lim _{x \rightarrow 2} f(x)\) exist? If so, what is it? If not, why not?
c. Find \(\lim _{x \rightarrow 4^{-}} f(x)\) and \(\lim _{x \rightarrow 4^{+}} f(x)\).
d. Does \(\lim _{x \rightarrow 4} f(x)\) exist? If so, what is it? If not, why not?
Equation Transcription:
{
Text Transcription:
f(x)= {x/2+1, x >2 3-x x<2
Lim_x right arrow 2^+f(x)
Lim_x right arrow 2^-f(x)
Lim_x right arrow 2^f(x)
Lim_x right arrow 4^-f(x)
Lim_x right arrow 4^+f(x)
Lim_x right arrow 4f(x)
ANSWER:SOLUTION
Step 1 of 5
Here, we have to determine the following limits.
Given
We know that when ,
and when
,
.