Question

Find all values xa where the function is discontinuous. For each value of x, give the limit of the function as x approaches a. Be sure to note when the limit doesn't exist.

Answer 1

The function y = 1/x is discontinuous at x = 0 and has limits approaching positive and negative infinity. For all other values of x, the function is continuous with a limit equal to the value itself.

Step-by-step explanation:

The function y = 1/x is discontinuous at x = 0 because division by zero is undefined. When x approaches 0 from the left (x < 0), the function y approaches negative infinity. When x approaches 0 from the right (x > 0), the function y approaches positive infinity. Therefore, the limit of the function as x approaches 0 doesn't exist.

For all other values of x, the function y = 1/x is continuous. The limit of the function as x approaches any other value is simply the value itself. For example, as x approaches 2, the limit of y = 1/x is 1/2.