Question

Find the least integer n such that f(x) is o(xn) for each of these functions. a) f(x) = 2x² x³ log x?

Answer 1

To find the least integer n such that f(x) is o(x^n) for the given function f(x) = 2x² x³ log x, we need to determine the highest power that dominates the function. The highest power that dominates the function is x³. Therefore, the least integer n such that f(x) is o(x^n) for f(x) = 2x² x³ log x is 3.

Step-by-step explanation:

To find the least integer n such that f(x) is o(x^n) for the given function f(x) = 2x² x³ log x, we need to determine the highest power that dominates the function.

Let's break down the function: f(x) = 2x² x³ log x

• The term 2x² grows faster than any logarithmic function.
• The term x³ grows faster than x².
• The term log x grows the slowest among the three.

Therefore, the highest power that dominates the function is x³.

Thus, the least integer n such that f(x) is o(x^n) for f(x) = 2x² x³ log x is 3.