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

f(x)={sqrt(x)(1+x sin((1)/(x))),x>0;-sqrt(-x)(1+x sin((1)/(x))),x<0;0,x, then f(x) is

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.

Let f(x)={(xsin(1/x), x ne 0),(k, x=0):} find k if f is continuous at x=0,

If f(x)={1/(1+e^(1//x)),\ \ \ \ x!=0 0,\ \ \ \ \ \ \ \ \ \ \ x=0 , then f(x) is continuous as well as differentiable at x=0 (b) continuous but not differentiable at x=0 (c) differentiable but not continuous at x=0 (d) none of these

If f(x)={(1)/(1+e^(1/x)),quad x!=00,quad x=0 then f(x) is continuous as well as differentiable at x=0 (b) continuous but not differentiable at x=0 (c) differentiable but not continuous at x=0 (d) none of these

Let f(x) = xe^-(1/|x|+1/x); x != 0, f(0) = 0 , test the continuity & differentiability at x = 0

Let f(x) = (xe)^(1/|x|+1/x); x != 0, f(0) = 0 , test the continuity & differentiability at x = 0

Let , f(x)=1/xsin(x^2) when x ne0 =0 when x=0 Discuss the continuity and differentiability of f(x) at x=0.

If f(x) = ((1+sinx)-sqrt(1-sinx))/(x) , x != 0 , is continuous at x = 0, then f(0) is