Finding the limit: x ^ - 1-e of LIM (x-0) (1 + x) divided by X

Finding the limit: x ^ - 1-e of LIM (x-0) (1 + x) divided by X


Let y = (1 + x) ^ (1 / x), LNY = ln (x + 1) / x = (x / (x + 1) - ln (x + 1)) / x ^ 2 = (x - (x + 1) ln (x + 1)) / (x ^ 2 (1 + x)) limy '= limylim (x - (x + 1) ln (x + 1)) / (x ^ 2 (1 + x)) = E



Limx tends to 0 (2 ^ x + 3 ^ X-2) / X=


Solving with lobida's law
We can get: LN2 + Ln3



Limx tends to 0 x ^ 3-1 / X-1


Original formula = LIM (x → 0) (x-1) (x ^ 2 + X + 1) / (x-1)
=lim(x→0) (x^2+x+1)
=1