You are here:

Calculus/Trig Limit solving with a square root

Advertisement

Expert: - 10/12/2008


Question
Hi- I am taking AP Calc BC, and I understand most of the work, but I am having trouble with solving for a limit using only the Limit Laws when there is a square root involved. The tricky question for me is:
        x
lim   --------
x->0  √(1+3x)-1

Thank you!

Answer
If we multiply the top and the bottom of the fraction by √(1+3x) + 1,
we get (x(√(1+3x) + 1)/[(√(1+3x) + 1)(√(1+3x) - 1)].

Note that the bottom is (a+b)*(a-b), which is aČ - bČ.
See that aČ=1+3x, bČ=1, so aČ-bČ= 3x.

The top is x√(1+3x) + 1).

The top and bottom can both be divided by x (since x=0 is only a limit - we're not actually there), and the answer can be obtained by putting in x = 0.

Thanks for the question and have a great day.

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.