Final answer:
The limits lim x→1- f(x) and lim x→1 f(x) are asking for the behavior of the function f(x) as x approaches 1 from the left and right sides, respectively. Using the function f(x) = 4x³ - 1, the limits can be calculated to be 3.
Step-by-step explanation:
The limits lim x→1- f(x) and lim x→1 f(x) are asking for the behavior of the function f(x) as x approaches 1 from the left and right sides, respectively.
To find lim x→1- f(x), we substitute x values slightly less than 1 into the function f(x) and observe the output values. In this case, we substitute values like 0.9, 0.99, and so on into f(x). Similarly, to find lim x→1 f(x), we substitute x values slightly greater than 1 into f(x). For example, we can substitute 1.1, 1.01, and so on into f(x).
Using the function f(x) = 4x³ - 1, we can calculate the limits as follows:
lim x→1- f(x) = lim x→1- (4x³ - 1) = 3
lim x→1 f(x) = lim x→1 (4x³ - 1) = 3