multiply numerator and denominator by ...
L'Hopital again ...
if we have:
lim(x to 1) ((x/(x-1)-1/lnx)
then we get:
lim(x to 1) ((xlnx-x+1)/(xlnx-lnx))
then we take x=1:
lim(x to1)((ln(1)+1-1) / (ln(1)-ln(1))
we get 0/0
and can apply LH:
How do we get NOW lim(x to1)((xlnx)/(xlnx+x-1)???
What is the inversion doing here?
In line 5, that's the same thing as the derivative of x*lnx-x+1. If you look at the definition of L'Hopital's Rule, it implies differentiation of the numerator and the denominator. Therefore, line 5 shows the derivative of the numerator and the denominator from line 4. Line 5 simply results from using L'Hopital's Rule.
Please, could anyone help me with this:
Find number a is element of R so that the function f(x)=a; x<=0
( x^1/2-1)/(x^1/3-1); x>0
is continuous in R?
p.s. how to get latex here? I tried to write by tags, but it just showed the source, what I wrote, and not the nice latex text!