At `x = 0`, `f(x) = cos x-1+x^2/2 - x^3/6`

Let f(x) = {{:((cos x-e^(x^(2)//2))/(x^(3))",",x ne 0),(0",",x = 0):} , then Statement I f(x) is continuous at x = 0. Statement II lim_(x to 0 )(cos x-e^(x^(2)//2))/(x^(3)) = - (1)/(12)

Let f(x) = {{:((cos x-e^(x^(2)//2))/(x^(3))",",x ne 0),(0",",x = 0):} , then Statement I f(x) is continuous at x = 0. Statement II lim_(x to 0 )(cos x-e^(x^(2)//2))/(x^(3)) = - (1)/(12)

Let f be a function defined on [-(pi)/(2), (pi)/(2)] by f(x) = 3 cos^(4) x-6 cos^(3) x - 6 cos^(2) x-3 . Then the range of f(x) is

If f(x) = cos x cos 2x cos 2^2 x cos^(2^3) x .....cos 2^(n-1) x and n gt 1 then f^(1)(pi/2) is

If f(x) = cos x\ cos 2x\ cos 2^2\ x\ cos 2^3 x\ ....cos2^(n-1) x and n gt 1, then f'(pi/2) is

If f (x) = |{:( sin x , cos x , tan x) , (x^(3) , x^(2) , x) , (2x , 1 , x):}| , then Lt_(x to 0) (f(x))/(x^(2))=