Final answer:
The limit as x approaches -1 of the function (x²)/(2x² - 1) is evaluated by direct substitution of -1 into the function, yielding a result of 1. The limit exists and is equal to 1.
Step-by-step explanation:
To evaluate the limit lim(x → -1) (x²)/(2x² - 1), we can directly substitute the value of x that x is approaching into the function, providing the function is continuous at that point. When x is -1, we can substitute -1 into the function:
- Substitute -1 for x: ((-1)²)/(2(-1)² - 1)
- Simplify the numerator: 1
- Simplify the denominator: 2(1) - 1 = 2 - 1 = 1
- Calculate the limit: 1/1 = 1
The limit exists and is equal to 1. Since the function is a rational expression and is continuous at x = -1, we simply evaluate the function at that point.