`lim_(x->0)8/(x^8)(1-cos(x^2)/2-cos(x^2)/4+cos(x^2)/2cos(x^2)/4)`

If lim_(x rarr 0)((1-cos((x^2)/2)-cos((x^2)/4)+cos((x^2)/2)cos((x^2)/4))/(x^8))=2^(-k) . Find k.

lim_(xto0) (1)/(x^12){1-cos (x^2/2)-cos (x^4/4)+cos (x^2/2) cos (x^4/4)} is equal to

Let a=min{x^(2)+2x+3,x in R} and b=lim_(xto0)(64)/(x^(4))[1-cos(x/2)-cos(x/4)+cos(x/2)cos(x/4)] then

Evaluate: (lim)_(x rarr0)(8)/(x^(8)){1-cos((x^(2))/(2))-cos((x^(2))/(4))+cos((x^(2))/(2))cos((x^(2))/(4))}

lim_(x rarr0)(1-(x^(2))/(2)-cos(x))/(x^(4))

lim_(x->0) (cos2x-cos4x)/(cos3x-cos5x) =

lim_(x-gt0)(cos2x-cos3x)/(cos4x-1)

lim_(x rarr0)x^(4)cos(2/x)

lim_(x rarr0)(sin^(2)4x+2cos^(2)x-2cos x)/(cos^(2)x-cos^(3)x)