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 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(x) given by f(x)={xsin1/x ,x!=0 0,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)={:{(x" sin "(1)/(x)", if "x!=0),(0" , if "x=0):} is continuous at x =0

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

Show that the function f(x)={{:(x"cos"(1)/(x),"when"xne0),(0,"when"x=0):} is continuous at x=0.

Show that f (x) = f(x) = {(x,sinfrac(1)(x)),(0,x=0):} is continuous at x = 0

Show that the function f(x)={{:((sinx)/(x)+cosx", if "x!=0),(2", if "x=0):} is continuous at x=0 .