Question

find discontinuity? if removable, define a new function that removes the discontinuity..

f(x)= x lnx^2
i get the topic just forgot ln. refresh my memory?

Answer 1

\(\ln y=x\Leftrightarrow y=e^x\)

Answer 2

Since \(e^x>0\) we can tell \(\ln y\) is undefined for \(y=0\)

Answer 3

that's right i got you, thanks!

Answer 4

no problem! that means our function is undefined at \(x=0\), hence there's our 'discontinuity'. To determine whether it's 'removable', see if our left and right limits match up... :-)