" शान नि॰र्ञा क्तित : "lim_(x rarr4)((cos alpha)^(x)-(sin alpha)^(x)-cos2 alpha)/(x-4)

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

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))

lim_(x rarr oo)sqrt((x+cos alpha)/(x+sin alpha))=

Evaluate the following limits (if exists), where {,} denotes the fractional part of x and [,] denotes the greatest integer part lim_(x rarr 4) [(cos alpha)^x-(sin alpha)^x-cos 2alpha]/[(x-4)], a in (0, pi//2)

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

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

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

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

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