Solution Found!
One-sided limits Let Find (a) and (b) then use limit
Chapter 2, Problem 52E(choose chapter or problem)
One-sided limits Let \(\text { Let } f(x)=\left\{\begin{array}{ll}x^{2} \sin (1 / x), & x<0 \\\sqrt{x}, & x>0\end{array}\right.\)
Find (a) \(\lim _{x \rightarrow 0^{+}} f(x)\) and (b) \(\lim _{x \rightarrow 0^{+}} f(x)\) ; then use limit definitions to verify your findings. (c) Based on your conclusions in parts (a) and (b), can you say anything about \(\lim _{x \rightarrow 0} f(x)\)? Give reasons for your answer.
Equation Transcription:
{
Text Transcription:
f(x)={x^2sin(1/x), x<0 sqrt x, x>0
Lim_x right arrow 0^+f(x)
Lim_x right arrow 0^-f(x)
Lim_x right arrow 0 f(x)
Questions & Answers
QUESTION:
One-sided limits Let \(\text { Let } f(x)=\left\{\begin{array}{ll}x^{2} \sin (1 / x), & x<0 \\\sqrt{x}, & x>0\end{array}\right.\)
Find (a) \(\lim _{x \rightarrow 0^{+}} f(x)\) and (b) \(\lim _{x \rightarrow 0^{+}} f(x)\) ; then use limit definitions to verify your findings. (c) Based on your conclusions in parts (a) and (b), can you say anything about \(\lim _{x \rightarrow 0} f(x)\)? Give reasons for your answer.
Equation Transcription:
{
Text Transcription:
f(x)={x^2sin(1/x), x<0 sqrt x, x>0
Lim_x right arrow 0^+f(x)
Lim_x right arrow 0^-f(x)
Lim_x right arrow 0 f(x)
ANSWER:
Solution :
Step 1 :
In this problem, we have to find the limit then verify answer by limit definition.