Question

I really need help with a l'Hospital's rule problem, please!

Answer 1

What is the limit as x is approaching 0 from the right of (-xlnx)

Answer 2

\[
\lim_{x \rightarrow 0^+}-x\ln(x) = -\lim_{x \rightarrow 0^+}\frac{\ln(x)}{1/x} = ?
\]

Answer 3

Apply L'H rule now because it is of the form infinity / infinity.

Answer 4

How did you get it in that form?

Answer 5

x can be written as \(\frac{1}{1/x}\)

Answer 6

Got it. Thank you! Can I ask you one more question?

Answer 7

go ahead.

Answer 8

How would I find the limit as x approached 0+ of x^(1/x)?

Answer 9

Let y = x^(1/x)
Take natural log on both sides:
ln(y) = 1/x * ln(x)
Now take the limit. Whatever limit you find, y = e^(that limit)

Answer 10

Thank you so much!!

Answer 11

You are welcome.