Show that the function `f(x)={xsin1/x\ \ \ ,\ \ \ \ w h e n\ x!=0 0\ \ \ \ \ \ \ \ \ \ \ w h e n\ x=0` is continuous but not differentiable at `x=0` .

Show that the function f(x)={x \ sin \ 1/x\ \ \ ,\ \ \ \ w h e n\ x!=0 \ \ \ \ \ \ \ 0, when \ \ \ x=0 is continuous but not differentiable at x=0 .

If f(x)={(sin3x)/x ,\ \ \ w h e n\ x!=0 1,\ \ \ w h e n\ x=0 . Find whether f(x) is continuous at x=0 .

Show that the function f(x) given by f(x)={xsin1/x ,x!=0 0,x=0

Let f(x)={(1-cosx)/(x^2),\ \ \ w h e n\ x!=0 ; 1,\ \ \ \ w h e n\ x=0 . Show that f(x) is discontinuous at x=0 .

Find the values of k for which f(x)={(1-cos4x)/(8x^2),\ \ \ w h e n\ x!=0k ,\ \ \ w h e n\ x=0 is continuous at x=0 .

Let f(x)=(1-cosx)/(x^2),\ \ \ w h e n\ x!=0,\ f(x)=1,\ \ \ w h e n\ x=0 . Show that f(x) is discontinuous at x=0 .

Show that f(x)={(x-|x|)/2,\ \ \ w h e n\ x!=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \2,\ \ \ w h e n\ x=0 is discontinuous at x=0 .

Show that the function f(x) = {:{(x^n sin(1/x), x ne 0),(0, x = 0):} is continuous but not differentiable at x= 0.

Show that the function f(x)=(x)/(1+e^(1//x),x ne 0, f(0)= 0 is continuous at x = 0

Show that f(x)={(|x-a|)/(x-a),\ \ \ w h e n\ x!=a \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \,\ \ \ w h e n\ x=a is discontinuous at x=a for any value of f(a)