[f(x)=[((x-2)^(3))/(a)]sin(x-2)+a cos(x-2)],[" If "quad " denotes G.I.F) in continous and "],[" differentiable in "(4,6)," then "]

In the function f(x)=[(x-2)^3/a]sin(x-2)+acos(x-2), (where [.] denotes the greatest integer function ) is continuous and differentiable in (4,6), then

Lt_(x rarr4^(+))(x^(2)-7x+12)/(x-[x]) =[ where [ ] denotes G.I.F.]

Evaluate int_(0)^(2pi) [ sin x + cos x] dx where [ ] denotes the G.I.F.

lim_(t rarr0)[min(x^(2)+4x+6)(sin t)/(t)] is equal to (where denotes the G.I.F )=

Show that the function f defined as follows f(x)={3x-2,0 2 is continous at x=2 but not differentiable.

If f (x) = (2x + 3 sin x )/(3x + 2 sin x ) , x ne 0 is continous at x = 0 then f (0) = ?

The value of int_((pi)/(4))^((pi)/(2))[sin x+[(2x)/(pi)]]dx where [.] denotes G.I.F.

If g(x)=log_(f^(2)(x))((f(x)-1)/(f(x)-2))+(3f(x)-3)^(20)+sin^(-1)((f(x))/(7))+sqrt(cos(sin f(x)))) where f(x) is a real valued function,then the range of f(x) for which g(x) is defined.