Question

What is the limit as h approaches 0 of (∛1+h)-1/h?

A) 0
B) 1
C) [infinity]
D) Does not exist

Answer 1

The limit as h approaches 0 of (∛1+h)-1/h is 1/3.

Step-by-step explanation:

To find the limit as h approaches 0 of (∛1+h)-1/h, we can start by simplifying the expression. Using the property of radicals, we have (∛1+h) = 1 + h/3 + O(h^2), where O(h^2) represents higher order terms. Now, we can substitute this into the expression and simplify: (∛1+h)-1/h = (1 + h/3 + O(h^2))-1/h = 1/h + (1/3) + O(h) - 1/h. Simplifying further, we have 1/h - 1/h + (1/3) + O(h) = 1/3 + O(h).