Evaluate `lim_(x->alpha) ((xsinalpha-alphasinx)/(x-alpha))`

lim_(x rarr oo)(sin alpha-alpha sin x)/(x-alpha)

If alpha is not an integral multiple of pi , then : lim_(x to alpha) ((sin x)/(sin alpha))^(1/(x-alpha) )=

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

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

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

If lim_(x to alpha) (alpha^x - x^alpha)/(x^alpha - alpha^alpha) = -1 then what is the value of alpha ?

lim_(alpha rarr(pi)/(4))(sin alpha-cos alpha)/(alpha-(pi)/(4))

The value of lim_(xto4)((cos alpha)^(x)-(sinalpha)^(x)-cos 2alpha)/(x-4), alpha epsilon(0,(pi)/2) is

lim_(x rarr00)(sin alpha x)/(sin beta x)=(alpha)/(beta)

Statement -1 : lim_(xrarralpha) sqrt(1-cos 2(x-alpha))/(x-alpha) does not exist. Statement-2 : lim_(xrarr0) (|sin x|)/(x) does not exist.