find the value of the value of the constant c such that the given function is continuous for all x
f(x) ={c^2-x^2, if x<0
........{2(x-c)^2, it x>=0
A function f(x) is continuous at x=a, if,
Left hand limit = right hand limit = f(a)
$\displaystyle \Rightarrow \mathop {\lim }\limits_{x \to a - } f\left( x \right) = \mathop {\lim }\limits_{x \to a + } f\left( x \right) = f\left( a \right) \hfill \\$
Now, try to solve by yourself.