Show that `f(x)= {(x^(3)+3",",x ne0),(1",",x=0):}` is a discontinuous function at x= 0.

Prove that f(x)= {((sin x)/(x)+ cos x ",",x ne 0),(2",",x=0):} is a continuous function 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?

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

Show that, f(x)= {((e^((1)/(x))-1)/(e^((1)/(x))+1)",",x ne 0),(0",",x=0):} . Is discontinuous at x= 0

f(x)= {((|sin x|)/(x)",",x ne 0),(1",",x=0):} Examine the continuity of f(x), x= 0

Show that f(x)={{:("x sin"(1)/(x)",","when",x ne 0),(0",","when",x = 0):} is continuous but not differentiable at x = 0

f(x)= {((tan 2x)/(x)",",x ne 0),(K",",x=0):} If a function f is continuous at x=0 then find k.

f(x)= {((x(1 + a cos x)-b sin x)/(x^(3))",",x ne 0),(0",",x=0):} . If f is continuous at x=0 then find the value of a and b.