if `f(x)=sin[x]/([x]+1) , x > 0` and `f(x)=(cospi/2[x])/([x]) , x < 0` and `f(x)=k , x=0` where `[x]` denotes the greatest integer less than or equal to `x,` then in order that the continuous at `x = 0,` the value of `k` is equal to

If f(x)=sin((1)/(x)), then at x=0

f (x) = (sin x )/(x) , x ne 0 and f(x) is continous at x = 0 then f(0) =

If f(x)=x sin(1/x), x!=0 then (lim)_(x->0)f(x)=

If f(x)=sin|x|-e^(|x|) then at x=0,f(x) is

If f(x)=sin|x|-e^(|x|) then at x=0,f(x) is

If f(x) is continuous at x=0 , where f(x)=(sin(x^(2)-x))/(x) , for x!=0 , then f(0)=

ind the value of a and b if f(x) is continuous at x=0. If f(x)={(sin(a+1)x+2sin x)/(2),x 0}

Deine F(x) as the product of two real functions f_1(x) = x, x in R, and f_2(x) ={ sin (1/x), if x !=0, 0 if x=0 follows : F(x) = { f_1(x).f_2(x) if x !=0, 0, if x = 0. Statement-1 : F(x) is continuous on R. Statement-2 : f_1(x) and f_2(x) are continuous on R.

Examine the continuity of f(x) at x=0 if f(x)= (sin 2x)/(2x), x ne 0