I need some help on this problem and limit, i have no idea how to complete it.
1. A train travels for 120 s between two stations. It accelerates for 30 s, maintains a constant velocity for 70 s, and brakes to a stop in 20 s. The velocity function v(t), with velocity measured in m/s, is defined as follows:
Determine the total distance travelled by the train in the 120-second time interval.
2. What is the limit of
Yeah, the limit gives 0/0 but this is undefined. So, the limit is what's of consequence not the actual function value. That means that it's not really determinant that they go to the same limit. It's the rate at which they converge to this limit respectively that makes a difference. This is exactly what L'Hospitals rule is for. Thieving jerk (L'Hospital, not any of you.)
Read this: http://www.macalester.edu/aratra/edi.../Lhospital.pdf
for the facts of the paid arrangement (contract) between l'Hospital and John Bernoulli ......
Getting off-topic a little bit ....... But for those interested:
Amazon.com: A Radical Approach to Real Analysis: Second Edition (Classroom Resource Materials): David M. Bressoud: Books
Amazon.com: A Radical Approach to Lebesgue's Theory of Integration (Mathematical Association of America Textbooks): David M Bressoud: Books