Show that the function f given by `f(x)= {{:(x^2+2," if "x ne 0),(1," if "x=0):}` is not continuous at x=0.

For what value of k is the function defined by f(x)={{:(k(x^(2)+2)," if " x le0),(3x+1," if "x gt 0):} continuous at x= 0? Also write whether the function is continuous at x=1.

The value of k which makes the function defined by : f(x) = {{:("sin" (1)/(x),"if",x ne 0),(k,"if",x = 0):} continuous at x = 0 is :

Is the function f defined by f(x) = {{:(x," if "x le 1),(3," if "x gt 1):} continuous at x= 0 ? At x=1? At x=2? .

For what value of lambda is the function defined by f(x)={{:(lambda(x^2 -2x)",",ifxle0),(4x +1",",ifx gt0):} continuous at x = 0 ?

Discuss the continuity of the function f given by {{:(x," if "x ge 0),(x^3," if "x lt 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?

The function f(x) = {{:((sin x)/(x) + cos x,"if",x ne 0),(k,"if",x = 0):} is continuous at x = 0, then value of k is :

Show that the signum function f : R to R given by f(x) = {(1, if, x gt 0),(0, if, x = 0),(-1, if, x lt 0):} is neither one-one nor onto.

Show that the function defined by f(x)= cos (x^2) is a continuous function.