lim_(x rarr0)(cos^(2)(1-cos^(2)(1-cos^(2)(......cos^(2)(x)))+...))/(sin[pi((sqrt(x+4)-2)/(x))])

Evaluate the following limits (if exists), where {,} denotes the fractional part of x and [,] denotes the greatest integer part lim_(x rarr 0) (cos^2(1-cos^2(1-cos^2.......cos^2(x)......)))/(sin[pi((sqrt(x+4) - 2)/x) ]

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

lim_(x rarr0)(sin^(2)x(1-cos2x))/(x^(2))

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

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

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

lim_(x rarr0)(cos x)/(x+2)

lim_(x rarr0)(cos x)/(x+2)

lim_(x rarr0)(cos2x-1)/(cos x-1)

lim_(x rarr0)(cos2x-1)/(cos x-1)