What is the Limit of xln(x) - x as x Approaches 0?

[blessedcurse]

Homework Statement

What is the value of xln(x)-x when x=0?

Homework Equations

I'm assuming you do L'Hopital's

The Attempt at a Solution

I'm assuming you factor out the x, leaving:

x(ln(x)-1)

but that's still not in the form of \frac{\infty}{\infty} or \frac{0}{0}

Would you do:

lim_{x\rightarrow\infty}\frac{(ln(x)-1)}{x^{(-1)}}

=lim_{x\rightarrow\infty}\frac{(1/x)}{1}

=0

??

 

[gabbagabbahey]

Homework Statement

What is the value of xln(x)-x when x=0?

Homework Equations

I'm assuming you do L'Hopital's

The Attempt at a Solution

I'm assuming you factor out the x, leaving:

x(ln(x)-1)

but that's still not in the form of \frac{\infty}{\infty} or \frac{0}{0}

Would you do:

lim_{x\rightarrow\infty}\frac{(ln(x)-1)}{x^{(-1)}}

=lim_{x\rightarrow\infty}\frac{(1/x)}{1}

=0

??

\lim_{x\to 0} x\ln(x)-x=(\lim_{x\to 0} x\ln(x))-(\lim_{x\to 0} x)