You are here:

Calculus/differential calculus

Advertisement

Expert: - 11/22/2010


Question
find the slope of a line tangent to the curve y=3x^2 at the point P (1.5,6.75)by finding the limit of the slopes of the secant lines PQ where Q has x-values 1,1.4,1.49,1.499. can you show me step by step. thanks

Answer
We are given x1 = 1, x2 = 1.4, x3 = 1.49, and x4 = 1.499.
With these we get y1 = 3(1^2) = 2, y2 = 3(1.4^2) = 3*1.96 = 5.82,
y3 = 3(1.49^2) = 3*2.2201 = 6.6603, y4 = 3(1.499^2) = 3*2.247001 =
6.741003.

At x0 = 1.5, y0 = 3(1.5^2) = 3*2.25 = 6.75.

To approximate the slope, compute (yi-y0)/(xi-x0)
for i = 1, 2, 3, and 4.

For i = 1, we get (2-6.75)/(1 -1.5) = -4.75/-0.5 = 9.5.
These can be continued for i = 2, 3, and 4.

Again, the x's are 1, 1.4, 1.49, and 1.499.
The matching y's are 2, 5.82, 6.6603, and 6.741003.
For each one, x0 = 1.5 and y0 = 6.75.

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.