lim_(x rarr0)(cos x)^(cot x)

If alpha = lim_(x rarr pi//4)""(tan^(3)x - tan x)/(cos (x + (pi)/(4))) and beta = lim_(x rarr 0)(cos x)^(cot x) are the roots of the equation, a x^(2) + bx -4 = 0 , then the ordered pair (a, b) is :

lim_(x rarr0)(xcotx)

lim_(x rarr0)(cos ecx-cot x)

lim_(x rarr0)(cotx)^(x)

lim_(x rarr0)(cot x)^(sin x)

lim_(x rarr0)(1+sin x)^(cot x)

lim_(x rarr0)(2-cotx)

Evaluate the following limit: (lim)_(x rarr0)(cos ecx-cot x)/(x)