Any ideas? lim X^{XX} x-> 0^{+} I know how to do x^x: lim X^{X} = lim e^{x * ln x} = e^{0} = 0 lim x * ln x = lim ln x / (1/x) = lim (1/x) / (-1/x^{2}) = lim -x = 0
Could you elaborate more? I alredy tried this method and got stuck with lim (ln x) * (x^x), i could not solve it
lim ln x * (x^x) = lim ln x * lim x ^ x = (- infinity) * 0 = 0 as X -> 0^{+} So you want to tell me that lim (X^x^x) = lim e^{x^x *ln x} = e^0 = 1? The limit suppose to be 0, .000001 ^ ( .000001 ^ .000001 ) = very very very small number (checked with calculator)
Well great! This is where I am stuck. lim ln x * x was solved by switching it to lim ln x / (1/x) and taking derivatives, with lim ln x * x/x it's not gonna work
e^{0} is not =0, but...........1.............. here is your mistake , hence ......limx^x=1 as x tends to 0 from the right And lim (ln x) * lim x^x = infinity multiplied by 1 and NOT by 0
[edited for content], in my solutions it was 1, but somehow I copied formula wrong and the whole time assumes lim x^x = 0. I spend way too much time studying for finals.... gotta take break