If `f(x) = { sqrtx(1+xsin(1/x)), x>0; -sqrt(-x)(1+xsin(1/x)), x<0; 0, x=0`, then `f(x)` is

If f(x)={sqrt(x)(1+xsin1/x), xlt 0 and -sqrt(-x)(1+xsin1/x) , x lt 0 , then f(x) is and 0 , x=0 continuous as well differentiable at x=0

Let f(x) ={{:(sqrt(x)(1+x sin (1//x)), xgt0),( - sqrt((-x))(1+ sin (1//x)), x lt 0),( 0, x=0):} Discuss differentiability at x=0.

If f(x)={(xsin,((1)/(x)),xne0),(0,,x=0):} Then, lim_(xrarr0) f(x)

If f(x)={(xsin,((1)/(x)),xne0),(0,,x=0):} Then, lim_(xrarr0) f(x)

If f(x)={xsin1/x , x!=0 0, x=0 , then (lim)_(x->0)f(x) equals a. 1 b . 0 c. -1 d. none of these

If f(0) = 2 , and f(x) = (1-cos kx)/(x.sin x) , x != 0 , is continuous at x = 0 , then : k =

Let g(x)=1+x-[x] and f(x)=-1 if x lt 0 =0 if x=0 then f[g(x)]= =1 if x gt 0

If f(x)={{:(xsin((1)/(x))", if "xne0),(0" , if "x=0):} then at x=0 the function f is