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Given f(x)=4-(1/2-x)^(2/3),g(x)={("tan"[...

Given `f(x)=4-(1/2-x)^(2/3),g(x)={("tan"[x])/x ,x!=0 1,x=0` `h(x)={x},k(x)=5^((log)_2(x+3))` Then in [0,1], lagranges mean value theorem is not applicable to (where [.] and {.} represents the greatest integer functions and fractional part functions, respectively). `f` (b) `g` (c) `k` (d) `h`

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Given f(x)=4-(1/2-x)^(2/3),g(x)={("tan"[x])/x ,x!=0 1,x=0 , h(x)={x}, k(x)=5^((log)_2(x+3)). Then in [0,1], lagranges mean value theorem is not applicable to (a) f (b) g (c) k (d) h (where [.] and {.} represents the greatest integer functions and fractional part functions, respectively).

Given f(x)=4-(1/2-x)^(2/3),g(x)={("tan"[x])/x ,x!=0 1,x=0 , h(x)={x}, k(x)=5^((log)_2(x+3)). Then in [0,1], lagranges mean value theorem is not applicable to (a) f (b) g (c) k (d) h (where [.] and {.} represents the greatest integer functions and fractional part functions, respectively).

Given f(x) = 4- ((1)/(2) - x)^(2//3) , g(x) = {:{((tan[x])/(x),","x cancel(=)0),(1,","x=0):}" "h(x)={x}, k (x) = 5^(log_(2)(x+3)) Then in [0,1], Lagrange's mean value theorem is not applicable to (where [.] and {.} represents the greatest integer functions and fractions part functions, respectively )

If (x)=[x],0<={x}<0.5 and f(x)=[x]+1,0.5<{x}<1 then prove that f(x)=-f(-x) (wherel.] and {.} represent the greatest integer function and the fractional part function, respectively).

If f(x) = [x] , 0<= {x} < 0.5 and f(x) = [x]+1 , 0.5<{x}<1 then prove that f (x) = -f(-x) (where[.] and{.} represent the greatest integer function and the fractional part function, respectively).

If f(x) = [x] , 0<= {x} < 0.5 and f(x) = [x]+1 , 0.5<{x}<1 then prove that f (x) = -f(-x) (where[.] and{.} represent the greatest integer function and the fractional part function, respectively).

If f(x) = [x] , 0<= {x} < 0.5 and f(x) = [x]+1 , 0.5<{x}<1 then prove that f (x) = -f(-x) (where[.] and{.} represent the greatest integer function and the fractional part function, respectively).

If f(x) = [x] , 0<= {x} < 0.5 and f(x) = [x]+1 , 0.5<{x}<1 then prove that f (x) = -f(-x) (where[.] and{.} represent the greatest integer function and the fractional part function, respectively).

Let f (x)= tan/x, then the value of lim_(x->oo) ([f(x)]+x^2)^(1/({f(x)})) is equal to (where [.] , {.} denotes greatest integer function and fractional part functions respectively) -

f:(2,3)rarr(0,1) defined by f(x)=x-[x], where [.] represents the greatest integer function.