Calculus/Limit's

Advertisement

Expert: - 3/14/2011


Question
Compute lim x->1 x^2-1/x^2+5x-6 algebraically with factoring and using l'Hopital's Rule

Answer
Note that (x²-1)/(x²+5x-6) = [(x-1)(x+1)]/[x+6)(x-1)].
Cancelling the (x-1) terms on the top and the bottom of the fraction gives (x+1)/(x+6).
Putting in x=1 gives the answer.

Now l'Hospital's Rule says if the numerator and the denominator both go to 0 or both go to infinity, they can each be differentiated.  That is, the derivative of x²-1 is 2x and
the derivative of x²+5x-6 is 2x+5, so the answer can also be found by putting x=1 into
the fraction 2x/(2x+5).

Both of the methods should give 2/7 as the answer.

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.