# 2 quick problems

• Jun 23rd 2008, 08:48 PM
wren17
2 quick problems
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:
http://www.mathhelpforum.com/math-he...64936cfd-1.gif
http://www.mathhelpforum.com/math-he...819a8487-1.gif
http://www.mathhelpforum.com/math-he...da8cef9c-1.gif

Determine the total distance travelled by the train in the 120-second time interval.

2. What is the limit of http://www.mathhelpforum.com/math-he...1eca7abb-1.gif
• Jun 23rd 2008, 11:58 PM
CaptainBlack
Quote:

Originally Posted by wren17
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:
http://www.mathhelpforum.com/math-he...64936cfd-1.gif
http://www.mathhelpforum.com/math-he...819a8487-1.gif
http://www.mathhelpforum.com/math-he...da8cef9c-1.gif

Determine the total distance travelled by the train in the 120-second time interval.

$s=\int_{t=0}^{120} v(t)\; dt = \int_{t=0}^{30} v(t)\; dt + \int_{t=30}^{100} v(t)\; dt + \int_{t=100}^{120} v(t)\; dt$

and that you should be able to do.

RonL
• Jun 24th 2008, 12:00 AM
wren17
Thanks i actually just started to figure that out, im still stuck with the limit though
• Jun 24th 2008, 12:04 AM
CaptainBlack
Quote:

Originally Posted by wren17

Lets assume you want the limit as x goes to zero. Well you could try either expanding the numerator as a power series about zero, or apply L'Hopital's rule (three times I think should do it).

RonL
• Jun 24th 2008, 12:06 AM
wren17
Ok, thats similar to what i was attempting but each time i would get stuck rather quickly
• Jun 24th 2008, 01:50 AM
wkrepelin
L'Hospital
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.)
• Jun 24th 2008, 02:20 AM
mr fantastic
Quote:

Originally Posted by wkrepelin
[snip]
This is exactly what L'Hospitals rule is for. Thieving jerk (L'Hospital, not any of you.)

Au contraire.

for the facts of the paid arrangement (contract) between l'Hospital and John Bernoulli ......
• Jun 24th 2008, 02:21 AM
mr fantastic
Quote:

Originally Posted by wren17
Ok, thats similar to what i was attempting but each time i would get stuck rather quickly

• Jun 24th 2008, 03:11 AM
CaptainBlack
Quote:

Originally Posted by mr fantastic
Au contraire.

for the facts of the paid arrangement (contract) between l'Hospital and John Bernoulli ......

Now there's a coincidence, the source of the pdf is a book (together with the Lesbegue Integral sequal) sitting in my shopping trolly at Amazon waiting for me to save enough to buy it (Speechless)

RonL
• Jun 24th 2008, 03:18 AM
CaptainBlack
Quote:

Originally Posted by wkrepelin
Thieving jerk (L'Hospital, not any of you.)

Not that different an arrangement than that offered by the "We write your thesis for you" people who regularly spamm this site (Punch)

RonL
• Jun 24th 2008, 05:21 PM
mr fantastic
Quote:

Originally Posted by CaptainBlack
Now there's a coincidence, the source of the pdf is a book (together with the Lesbegue Integral sequal) sitting in my shopping trolly at Amazon waiting for me to save enough to buy it (Speechless)

RonL

lol! Mine too, now (do you get paid a commission, Captain?)

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