Question

URGENT! Exam, need to calculate lim x^x as x approaches 0+

Answer 1

\[\lim_{x \rightarrow 0^{+}} x ^{x}\]

Answer 2

2nd question) Need to calculate rate of change of length of square whose area equal to 100m2, where rate of change \[\frac{ dA }{ dt }=1 \frac{ m ^{2} }{ s }\]

Answer 3

\[\lim_{x \rightarrow 0^{+}} x ^{x}=L\]
\[\lim_{x \rightarrow 0^{+}} \ln(x ^{x})=\ln(L)\]
\[\lim_{x \rightarrow 0^{+}} x\ln(x)=\ln(L)\]

Answer 4

\[
x\ln(x) = \frac{\ln(x)}{x^{-1}}
\]

Answer 5

You can use l'Hospitals at that point.

Answer 6

combinig with implicit differentiation?

Answer 7

?? I don't know what you mean.

Answer 8

that equals to 0?

Answer 9

Yes, but that gives you the equation \[
0=\ln(L)
\]And you really want to find \(L\) remember?

Answer 10

so our L is equal to 1?

Answer 11

Yeah!

Answer 12

great thx)

Answer 13

what about second question?))

Answer 14

Close this question and ask your next one in a new quesiton.

Answer 15

ok