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piecewise function Continuous

Petrus

Well-known member
Feb 21, 2013
739
Hello MHB,
If I want to decide constant a and b so its continuous over the whole R for this piecewise function

basicly what I got problem with is that \(\displaystyle x^{1/3}\) is not continuous for negative value so it will never be continuous for any value on constant a,b. I am missing something? or do they mean \(\displaystyle \frac{1}{8}\) and not \(\displaystyle -\frac{1}{8}\)

Regards,
\(\displaystyle |\pi\rangle\)
 

Amer

Active member
Mar 1, 2012
275
Hello MHB,
If I want to decide constant a and b so its continuous over the whole R for this piecewise function

basicly what I got problem with is that \(\displaystyle x^{1/3}\) is not continuous for negative value so it will never be continuous for any value on constant a,b. I am missing something? or do they mean \(\displaystyle \frac{1}{8}\) and not \(\displaystyle -\frac{1}{8}\)

Regards,
\(\displaystyle |\pi\rangle\)
In fact
[tex] \sqrt[3]{x} [/tex] is defined for all real numbers but the problem is in
[tex] \sqrt[n]{x} [/tex] with n even number
for a function to be continuous at a point c
[tex] \lim_{x \rightarrow c^- } f(x) = \lim_{x\rightarrow c^+ } f(x) = f(c) [/tex]
 

Petrus

Well-known member
Feb 21, 2013
739
In fact
[tex] \sqrt[3]{x} [/tex] is defined for all real numbers but the problem is in
[tex] \sqrt[n]{x} [/tex] with n even number
for a function to be continuous at a point c
[tex] \lim_{x \rightarrow c^- } f(x) = \lim_{x\rightarrow c^+ } f(x) = f(c) [/tex]
Thanks for the fast respond you are totally correct! I confused myself! Have a nice day!

Regards,
\(\displaystyle |\pi\rangle\)