`underset(x→∞)lim cos log((x-1)/x)`

underset(x to 0)(lim) (1-cos x)/(x) is :

lim_(x->oo) cos log((x-1)/(x))

Find the limits: (a) underset(x to 0)lim (arc cos (1-x))/sqrtx (b) underset(x to pi//4)lim (ln tan x)/(1-cot x) (c ) underset(x to 0) lim(1)/(sin x) ln (1+a sin x)

Find the limits: (a) underset(x to 0)lim (1-cos x)/(x^2) (b) underset(x to 0)lim (tanx-sinx)/(x^(3)) (c ) underset(x to 1)lim ""(cos (pix//2))/(1-x)

underset(x to 1)lim (log_(2) 2x)^(log_ x^( 5)) is equal to

underset(x to oo)lim (cos""2/x)^(x^2)=

underset(x to 1)lim (sqrt(1-cos 2(x-1)))/(x-1)