You are here:
- Home
- Teens
- Homework/Study Tips
- Calculus
- Mathematics (Calculus)
Calculus/Mathematics (Calculus)
Advertisement
Question
I am troubled in this question.
If f(x) = │x-1│-│x│ then discuss continuity and differentiability of f(x) at x=0 and x=1
Thanks in Advance
Continuity
---------------------
The value is continuous everywhere.
The points to check to make sure this is true are when the values inside | | change sign.
The left and right limits as x->1 of |x-1| are both 0, and so is the value at x=1.
The left and right limits as x->0 of |x| are both 0 and so is the value at x=0.
Thus, the function is continous.
The function is then
f(x) = 1 for x < 0,
f(x) = 1 - 2x 0<x<1, and
f(x) = 1 for x > 1
Differentiability
---------------------
f'(x) = 0 for x < 0,
f'(x) = -2 for < x < 1, and
f'(x) = 0 for 1 < x.
Thus at the points 0 and 1, the derivative on one outside is 0 and on the inside, it's -2.
Therefore at the points x=0 and x=1, the derivative does not exist.
- Add to this Answer
- Ask a Question
| Rating(1-10) | Knowledgeability = 10 | Clarity of Response = 10 | Politeness = 10 |
| Comment | Thank you sir, I picked all that what you have write,but still i have one problem 1) When f(x)= lim x0 x-1 where x approaching from left and right sides what answer it gives? 2) When f(x)= lim x1 x-1 where x approaching from left and right sides what answer it gives? 3) When f(x)= lim x0 x where x approaching from left and right sides what answer it gives? 4) When f(x)= lim x1 x where x approaching from left and right sides what answer it gives? | ||
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.