Final answer:
To find the one-sided limits of the function y = 1/x, we evaluate the function as x approaches from the left side (x < 0) and from the right side (x > 0). The left-hand limit approaches negative infinity, while the right-hand limit approaches positive infinity.
Step-by-step explanation:
The given function is y = 1/x. We are asked to find the one-sided limits.
To find the left-hand limit, we need to evaluate the function as x approaches from the left side (x < 0). Substitute x = -1, -0.1, -0.01, -0.001, and so on into the equation and find the corresponding values of y.
To find the right-hand limit, we need to evaluate the function as x approaches from the right side (x > 0). Substitute x = 1, 0.1, 0.01, 0.001, and so on into the equation and find the corresponding values of y.
As we substitute smaller and smaller positive values for x, the value of y becomes larger and larger, approaching positive infinity. As we substitute smaller and smaller negative values for x, the value of y becomes larger and larger, but negative, approaching negative infinity.