Show that the funcation ` f(x) = {{:( sinx",", if , x lt 0),( x"lt", if, x ge 0):} ` is continuous.

Show that the function f(x) = {{:(2 + x"," , "if " x ge 0),(1",", "if " x lt 0):} is not continuous at x = 0

Discuss the continuity of the function f(x) = {{:( (sin x)/x",", if , x lt 0),( (x+1)",", if , x ge 0):}

show that f(x) ={{:( (2x-1)",",if , x lt2),( (3x)/2",,if x ge 2):} is continuous

Determine the value of the constant k , so that the function f(x) ={ (kx)/|x| , if x lt 0 ,3 if x ge 0 is continuous at x=0

Show that the function f(x) ={{:( (7x+5)",","when" x ge 0), (( 5-3x)",", "when", x lt 0):} is a continuous function.

Prove that the function f(x) = {:{((sinx)/x , x < 0),(x^2 +1, x ge0):} is continuous.

{{:((x)/(|x|)","if x lt 0 ),(-1"," if x ge 0 ):}

Discuses the continity of the funcation f(x) ={{:( 2x-1",", if, x lt 0),( 2x +1",", if, x ge 0):}

Let f(x) = {{:( x, if , x ge 1),( x^(2), if , x lt 1):} is f a continuous function ? Why ?

If f(x)={:{((sinx)/(x)", for " x lt 0),(x+1", for " x ge 0):} , then