Question

Find the limit of 3x^(2x) as x approaches 0+.

Answer 1

if the variable=0 only the constant remains

Answer 2

you can't just plug in 0 because that gives\[3(0)^{0}\]and\[0^0\] is (usually considered) undefined

Answer 3

You mean \(0^0\) isn't indeterminate? Woah.

Answer 4

Why did I think it was? Let me check...

Answer 5

I would do something like \[
3x^{2x} = 3\exp(\ln(x^{2x})) = 3\exp(2x\ln(x)) = 3\exp\left(\frac{2\ln(x)}{x^{-1}}\right)
\]

Answer 6

Or maybe that should be \(2x/[\ln(x)]^{-1}\), so that it is another indeterminate form we can l'Hospital, rather than infinity / undefined.