Question

What is the rate of convergence of ln(1 h) to 0 as h approaches 0 ?

Answer 1

The rate of convergence of ln(1 + h) to 0 as h approaches zero is first-order, meaning ln(1 + h) approaches 0 linearly.

Step-by-step explanation:

The rate of convergence of ln(1 + h) to 0 as h approaches 0 can be analyzed using calculus, specifically by finding the limit of the natural logarithm function as h goes to 0. The function ln(1 + h) approaches 0 linearly as h approaches 0, and this can be shown using L'Hopital's rule, where the derivative of the numerator and denominator are taken, resulting in the limit of h/h which equals 1. Therefore, ln(1 + h) has a first-order convergence towards 0 as h goes to zero.