Limx → x power of 0 e - x power of - E / X

Limx → x power of 0 e - x power of - E / X

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

What is limx SiNx divided by X to the third power
Steps to take

Simultaneous derivation
The molecule 1-cosx is rewritten as 2Sin & sup2; (x / 2)
Denominator 3x & sup2; rewrite to 12 * (x / 2) & sup2;
Replace X / 2 with T
The original formula is equal to 1 / 6

Find the power of limx -'0 (1-sinx) Cotx
Cotx is the symbol of the square
Please list the equations,

(1-sinx) Cotx power denoted as (1-sinx) ^ (Cotx), then the original formula = (1-sinx) ^ (cosx / SiNx), here I Lim omit = {[1 + 1 / (1 / - SiNx)] ^ (1 / - SiNx)} ^ (- cosx) notice that the important limit (1 + 1 / x) ^ x tends to e, when x tends to infinity, and 1 / - SiNx tends to infinity, when X - tends to 0, so Lim [...]

Limx tends to 0 ((1 + x) ^ (1 / x) - E) / SiNx limit

Solution
 
＝－e/2.
The second half of the problem can also be calculated by the law of Robida