You are here:
Calculus/CALCULUS
Advertisement
Question
EVALUATE THE FOLLOWING INTEGRAL
1 $e^-x
draw rough sketch of the following
1 1 - e^-x
The derivative of e^f(x) is e^f(x)*f'(x).
In the first one, f(x) is only -x and we can see that f'(x) is a constant. The answer to the integral would be divided by f'(x). Since we have no limits, add on C, the unknown constant.
To draw the curve, consider the following.
What is the value at 0?
What is the value at infinity?
What is the value at -infinity?
Check the first derivative equal to zero for any local max or min.
Check the second derivative being zero for any inflection points.
Check the sign of the second derivative to see if the function is concave up or concave down.
With this information, you should be able to do a rough sketch of the curve.
Related Articles
Answers by Expert:
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.