Is f defined by `f(x)={{:((sin2x)/(x),"if "xne0),(1,"if "x=0):}" continuous"0` ?

Is f defined by f(x) = {((sin 2x)/x, if x != 0),(1, if x = 0):} continuous at 0?

Check the continuity of the function ‘f defined by f(x)= {{:((sin2x)/(x),if x ne 0),(1,if x=0):} at x=0

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

Check the continuity of the functionn 'f' defined by fx={{:((sin2x)/(x),if, x ne0),(x,if,x=0):}at x=0

Examine the continuity of f, where f is defined by f(x)={{:(sin x-cos x," if "x ne 0),(-1," if "x= 0):} .

Show that the function f given by f(x)= {{:(x^3+3," if "x ne 0),(1," if "x=0):} is not continuous at x=0.

Check the continuity of the function ‘f defined by f(x)={{:(cos x,if x ne 0),(1 ,if x=0):} at x=0