You are here:

Calculus/L'Hopital's Rule

Advertisement

Expert: Scotto - 6/21/2009


Question

What is a necessary condition for L'Hôpital's Rule to work?
A) The function must be determinate.
B) The function must be indeterminate.
C) The function must be inconsistent.
D) The function must possess at least three non-zero derivatives.


Answer
To state L'Hôpital's Rule, it says that if
lim x->c f(x) = lim x->c g(x) = 0 or
lim x->c g(x) = ±∞ and and the lim x->∞ f'(x)/g'(x) exists,
then limx->c f(x)/g(x) = limx->c f'(x)/g'(x).

Since L'Hôpital's Rule involves limits,
(B) and (C) can be seen to be wrong just by reading them.

In order for L'Hôpital's Rule to work, the function must be continous.  Also, it must be consistent for the limit to exist.

(D) can also be seen to not be true since we don't care how many zeroes the derivative has.  The only condition that we need is for the numerator and the denominator to both go to zero or both go to ∞.

This leaves the only choice as (A).

To check and make sure this is true, lets look up determinate.
What determinate means is that the function has defined limits.

Calculus

All Answers

Answers by Expert:

Ask Experts

Volunteer

Scotto

Expertise

Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.

Experience

Experience in the area: I have tutored students in all areas of mathematics for over 25 years. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

Publications
Maybe not a publication, but I have respond to well oveer 7,500 questions on the PC. Well over 2,000 of them have been in calculus.

Education/Credentials
I aquired well over 40 hours of upper division courses. This was well over the number that were required. I graduated with honors in both my BS and MS degree from Oregon State University. I was allowed to jump into a few junior level courses my sophomore year.

Awards and Honors
I have been nominated as the expert of the month several times. All of my scores right now are at least a 9.8 average (out of 10).

Past/Present Clients
My past clients have been students at OSU, students at the college in South Seattle, referals from a company, friends and aquantenances, people from my church, and people like you from all over the world.

©2012 About.com, a part of The New York Times Company. All rights reserved.