Hello all:

I have been studying a little traffic flow because of having been in road construction I never dreamed it was so involved, mathematically.

Here's a problem:

Suppose we are interested in the change in the number of cars N(t) between two observers, one fixed at x=a and the other moving in some prescribed manner, x=b(t).

The derivative of an integral with a variable limit is

Show this result using either considering:

or by using the chain rule for derivatives.

Also, Using , show that

I must admit, I am rather stymied. I ahve been going thorugh a rough time and I am having a difficult time concentrating.