Final answer:
To evaluate the limit lim x→1- g(x), plug in values of x less than 1 into the function and observe the trend of the output. In this case, as x approaches 1 from the left side, g(x) approaches -1.
Step-by-step explanation:
To evaluate the given limit lim x→1- g(x), we need to determine the behavior of the function g(x) as x approaches 1 from the left side. This means we consider values of x that are slightly less than 1. By plugging in values of x that are close to 1 but smaller than 1 into the function, we can observe the trend of the output. If the function approaches a specific value as x gets arbitrarily close to 1, then the limit exists and is equal to that value.
Let's consider an example. Suppose g(x) = x² - 1. Evaluating the function for x values less than 1, we have:
- When x = 0.9, g(0.9) = 0.9² - 1 = 0.81 - 1 = -0.19
- When x = 0.99, g(0.99) = 0.99² - 1 = 0.9801 - 1 = -0.0199
- When x = 0.999, g(0.999) = 0.999² - 1 = 0.998001 - 1 = -0.001999
From these values, we can see that as x approaches 1 from the left side, g(x) approaches -1. Therefore, the limit lim x→1- g(x) exists and is equal to -1.