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

Show that the function f(x) given by f(x)={(xsin(1/x),x!=0),(0,x=0):} is continuous at x = 0

Show that the functions f(x) given by f(x)={x(sin1)/(x),quad x!=00,quad x=0 is continuous at x=0

Show that the function f(x) given by f(x)={(sin x)/(x)+cos x,x!=0 and 2,x=0 is continuous at x=0

Show that the function f(x) given by f(x)={(sinx)/x+cosx ,x!=0 and 2,x=0 is continuous at x=0.

Show that the function f(x) given by f(x)={(sinx)/x+cosx ,\ \ x!=0 2,\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x=0 is continuous at x=0 .

Show that the function f(x) given by f(x)={:{(x" sin "(1)/(x)", if "x!=0),(0" , if "x=0):} is continuous at x =0

Show that function f(x) given by f(x)={(x sin(1/x),,,x ne 0),(0,,,x=0):} is continuous at x=0

Show that the function f given by f(x)={x^3+3ifx!=0 1ifx=0 is not continuous at x = 0 .

Show that the function f given by f(x)={x^(3)+3 if x!=0quad 1 if x=0 is not continuous at x=0

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