" Find "lim_(x rarr alpha)(x sin alpha-alpha sin x)/(x-alpha)

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

sin3 alpha=4sin alpha sin(x+alpha)sin(x-alpha)

sin 3 alpha = 4 sin alpha sin(x + alpha) sin(x-alpha)

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

lim_(x rarr2)((cos alpha)^(x)+(sin alpha)^(x)-1)/(x-2)

sin3alpha = 4 sin alpha sin(x+alpha)sin(x-alpha)

Prove that lim_(x rarr4)((cos alpha)^(x)-(sin alpha)^(x)-cos2 alpha)/(x-4)=cos^(4)alpha ln(cos alpha)-sin^(4)alpha,alpha in(0,(pi)/(2))

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

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