Show that ` g (x) = {{:( x^(2) " if " x le 1), ( x " if " x gt 1):}` is continuous or R .

Show that f(x)={{:(x^(2),if, 0 le x le 1),(x ,if, 1 le x le 2):} is continuous on [0,2]

f(x) = {{:(x " if " x le 1),(log x " if " x gt 1 ):} " then f (x) at x = 1 is "

Find k if the function is continuous at x=(pi)/(2) if (a) f(x)={{:((k cos x )/(pi-2x),x ne (pi)/(2)),(3,if x=(pi)/(2)):} at x=(pi)/(2) (b) f(x)={{:(kx+1, if x le 2),(cos x,if x gt 2):} at x=2 (c ) if f(x)={{:(k^(2)x-k,if x le 1),(2 , if x lt 1):} is continous on R then find the value (s) of k

Is the function defined by f(x)={{:(x+5," if "x le1),(x-5," if "x gt 1):} a continuous function?

Is the function f, defined by f(x) = {(x^2, if x le1),(x, if x > 1):} continuous on R?

For what value of lambda is the function defined by f(x)={{:(lambda(x^(2)-2x)," if "x le 0),(4x+1," if "x gt 0):} continuous at x= 0? What about continuity at x =1?

For what value of lambda is the function defined by f (x) f(x)={{:(lambda (x^(2)-2x),if x le0),(4x+1,if x gt0):} is continuous at x = 3