Find the value of a constant V so that the function k(x) is continuous for all x k(x)= ) x+v&xlt 0 4-x^2&xgeqslant 0

To ensure that the function is continuous for all , the left-hand limit and the right-hand limit at must be equal. First, let's find the left-hand limit as approaches 0: Next, let's find the right-hand limit as approaches 0: For to be continuous at , the left-hand limit and the right-hand limit must be equal. Therefore, we set them equal to each other and solve for : So, the value of the constant that makes the function continuous for all is .