`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)={{:(,x^(n)sin\ (1)/(x),x ne 0),(,0,x=0):} Then f(x) is continuous but not differentiable at x=0 . If

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

Let f(x)= {{:(1+ sin x, x lt 0 ),(x^2-x+1, x ge 0 ):}

Let f(x)={{:(x sin.(1)/(x)",",x ne0),(0",",x=0):}} and g(x)={{:(x^(2)sin.(1)/(x)",", x ne 0),(0",", x=0):}} Discuss the graph for f(x) and g(x), and evaluate the continuity and differentiabilityof f(x) and g(x).

Show that the function f(x)={ x^2sin(1/x) , when x !=0 and 0 when x=0 } is differentiable at x=0.

If f(x)={{:(,x^(m)sin((1)/(x)),x ne 0),(,0,x=0):} is a continous at x=0, then

Let f (x) = {{:(e ^((1)/(x ^(2)))sin ""(1)/(x), x ne0),(lamda, x =(0):}, then f '(0)

If f (x) = sqrt((1+ sin ^(-1) x)/(1- tan ^(-1)x)), then f (0) is equal to :

Let f(x)={{:(x^(n)sin(1//x^(2))","xne0),(0", "x=0):},(ninI). Then

Let f(x)={0 for x=0 x^2 sin (pi/x) for -1 1 or x <-1