" 1."lim_(alpha rarr0)(tan alpha-sin alpha)/(alpha^(3))

lim_(alpha rarr 0) (tan alpha- sin alpha)/alpha^3

Let m and n be two positive integers greater than 1. If lim_(alpha rarr0)(e^(cos alpha^(n))-e)/(alpha^(m))=-((e)/(2)) then the value of (m)/(n) is

lim_(x rarr0)(sin(alpha+x)-sin(alpha-x))/(cos(alpha+x)-cos(alpha-x))

The value of lim_(x rarr0)(sin alpha x-sin beta x)/(e^(alpha x)-e^(beta x))

lim_(x rarr0)(tan x)/(sin^(2)x)

The value of lim_(x rarr0)(sin alpha x+sin beta x)/(e^(alpha x)-e^(beta x)) equals

lim_(x rarr0)(sin alpha x)/(tan beta x)

lim_(x rarr0)(a^(sin x)-1)/(sin x)

lim_(x rarr0)(tan x^(3))/(x)

lim_(h rarr0)h sin(1/h)