Examine that ` f(x) = sin |x|` is a continuous function.

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

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

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

Prove that the function defined by f(x)= tan x is a continuous function.

Is the function defined by f(x)= |x| , a continuous function?

Let f be function satisfying f(x+y)=f(x)+f(y) and f(x)=x^(2)g(x) , for all x and y, where g(x) is a continuous function. Then f'(x) is :

If f(x) = ((e^(x)-1)^(4))/(sin((x^(2))/(lambda^(2)))log(1+(x^(2))/(2))), x ne 0 and f(0) = 8 be a continuous functions, then lambda equals :

Find the value of K so that the function f(x) = {{:(kx+1,"if"x le 5),(3x-5,"if"x ge5):} at x=5 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?