Finding the limit of (ln1 / x) ^ x when x approaches 0 from the right

Finding the limit of (ln1 / x) ^ x when x approaches 0 from the right

Let t = 1 / x, then
When x → 0 +, t → + ∞
∴lim(x→0+) (ln1/x)^x
=lim(t→+∞) (lnt)^(1/t)
=e^lim(t→+∞) ln[(lnt)^(1/t)]
=e^lim(t→+∞) [ln(lnt)]/t
=E ^ LIM (t → + ∞) 1 / (tlnt). L'Hospital Rule
=e^0
=1

When x approaches 0, find the limit LIM ((1 + 2tanx) ^ (1 / x)),

No equivalent infinitesimal substitution or lobita derivation is needed. As long as the basic limit solution is as follows, click to enlarge it

Let {x} be bounded and limy = 0, prove that limxy = 0

Because the sequence {x} is bounded, let X be the absolute value