Determine if f defined by`f(x)={x^2sin1/x , ifx!=0 0, ifx=0`

Determine if f defined by f(x)={x^2sin1/x , if""x!=0 0, if""""x=0

Determine if f defined by : f(x)={{:(x^(2)"sin"1/x", if "xne0),(0", if "x=0):} is a continuous function ?

Let f be defined on R by f(x)=x^(4)sin(1/x) , if x!=0 and f(0)=0 then (a) f'(0) doesn't exist (b) f'(2-) doesn't exist (c) f'' is not continous at x=0 (d) f''(0) exist but f''' is not continuous at x=0

Examine the continuity of f ,where f is defined by f(x)={sin x-cos x,quad if x!=0;-1, if x=0

Let f be defined on R by f(x)= x^(4)sin(1/x) , if x!=0 and f(0)=0 then (a) f'(0) doesn't exist (b) f'(2-) doesn't exist (c) f'' is not continous at x=0 (d) f''(0) exist but f'' is not continuous at x=0

Let f:RrarrR be function defined by f(x)={(sin(x^2)/2, ifx!=0),(0,if x=0):} Then, at x=0, f is

Let f:R rarr R be defined by f(x)={x+2x^(2)sin((1)/(x)) for x!=0,0 for x=0 then

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

If the function f(x) defined by {:(f(x),=x (sin)1/x,",","for"x != 0),(,=k, ",","for"x = 0):} is continuous at x = 0, then k =