Question

Find the limit as x tends to 0+:
lim(sqrt(x)*ln(x))

Answer 1

not sure if this is best answer, but if you assume 0^0 = 1 , then the limit is 0
\[\lim_{x \rightarrow 0+}\sqrt{x} \ln x = \ln e^{\lim_{x \rightarrow 0+}\sqrt{x} \ln x} = \ln \lim_{x \rightarrow 0+}x^{\sqrt{x}} = \ln 1 = 0\]

Answer 2

Hmm. Not sure how you got from the 2nd to the 3rd stage.

Answer 3

Although that is the right answer

Answer 4

I think I get it - does the \[e ^{\ln x}\] cancel out?

Answer 5

oh sorry, yes e^lnx = x

Answer 6

\[e^{\ln x * \sqrt{x}} = (e^{\ln x})^{\sqrt{x}} = x^{\sqrt{x}}\]

Answer 7

Thanks!
Here's your hard-earned "best response"

Answer 8

haha thx