G.I.F. , fractional part function

Questions on G.I.F || fractional part function ,trancedental function

Let veca=i+j+k.vecb={x}i+{sinx}j.vecc=c_1 i+c_2 j+c_3 k,|vecc|=1,(veca,vecb)=pi/4, veca and vecb are perpendicular to c.(Here [.] is G.I.F, {.} is fractional part function). Let f(x)=[veca(vecb xx vecc)]^2,A=[1,pi/4,pi/2,2,(2pi)/3,3}.A number is selected at random from A. If f is discontinuous at that number then the probability that f has local minimum is

Let g be a function defined by g(x)=sqrt({x})+sqrt(1-{x}) .where {.} is fractional part function, then g is

Range of the function f(x)=cos^(-1)(-{x}) where {.} is fractional part function,is:

prove "lim"_(xvecoo)(ln x)/([x])="lim"_(xvecoo)([x])/(ln x) where [.] is G.I.F. & {.} denotes fractional part function

The value of flim_(n->oo){(sqrt(2)+1)^n}(-1)^[[(sqrt(2)+1)^(n)], n in Z is (where[.] denotes G I F and {.} denotes fractional part function)

Find the range of f(x)=x-{x} , where {.} is the fractional part function.

The domain of function f(x)=ln(ln((x)/({x}))) is (where f ) denotes the fractional part function

The domain of function f(x)=ln(ln((x)/({x}))) is (where f ) denotes the fractional part function

Let f(x) = x - x^(2) and g(x) = {x}, AA x in R where denotes fractional part function. Statement I f(g(x)) will be continuous, AA x in R . Statement II f(0) = f(1) and g(x) is periodic with period 1.