- #1
tarheelborn
- 123
- 0
Homework Statement
What property of limits says that lim 2^(1/n) = 2^lim (1/n) = 2^0 = 1? Thanks.
The notation "Lim" stands for limit, which represents the value that a function approaches as its input approaches a given value. In this case, as the exponent (1/n) approaches 0, the value of the function 2^(1/n) approaches 1.
The exponent (1/n) represents a variable power, where n is a positive integer. This means that as n increases, the value of the function decreases. In the limit, as n approaches infinity, the value of the function approaches 1.
The value of the limit will change depending on the base of the function. For example, if the base is changed to 3, the limit will become 3^0 = 1. This is because the limit only depends on the behavior of the function near the given value, not on the value itself.
Yes, the limit can be approximated using numerical methods such as graphing or using a calculator. As n approaches 0, the value of the function will become increasingly closer to 1.
The limit of 2^(1/n) is equal to 1 because as n approaches 0, the exponent approaches 0. Any number raised to the power of 0 is equal to 1, so the limit of the function is 1.